Machine learning based subresolution assist feature placement

ABSTRACT

A method for training a machine learning model to generate a characteristic pattern, the method includes obtaining training data associated with a reference feature in a reference image. The training data includes (i) location data of each portion of the reference feature, and (ii) a presence value indicating whether the portion of the reference feature is located within a reference assist feature generated for the reference feature. The method includes training the machine learning model to predict a presence value based on the actual presence value in the training data. The predicted presence value indicates whether a portion of a feature (e.g., a skeleton point on a skeleton of a contour of the feature) is to be covered by an assist feature. The training is performed based on the training data such that a metric between a predicted presence value and the presence value is minimized.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority of U.S. application 62/984,396 whichwas filed on Mar. 3, 2020 and which is incorporated herein in itsentirety by reference.

TECHNICAL FIELD

The description herein relates generally to patterning process, and moreparticularly, apparatuses, methods, and computer program products forusing machine learning for placement of subresolution assist features incharacteristic patterns corresponding to a design layout.

BACKGROUND

A lithographic projection apparatus can be used, for example, in themanufacture of integrated circuits (ICs). In such a case, a patterningdevice (e.g., a mask) may contain or provide a pattern corresponding toan individual layer of the IC (“design layout”), and this pattern can betransferred onto a target portion (e.g. comprising one or more dies) ona substrate (e.g., silicon wafer) that has been coated with a layer ofradiation-sensitive material (“resist”), by methods such as irradiatingthe target portion through the pattern on the patterning device. Ingeneral, a single substrate contains a plurality of adjacent targetportions to which the pattern is transferred successively by thelithographic projection apparatus, one target portion at a time. In onetype of lithographic projection apparatuses, the pattern on the entirepatterning device is transferred onto one target portion in one go; suchan apparatus is commonly referred to as a stepper. In an alternativeapparatus, commonly referred to as a step-and-scan apparatus, aprojection beam scans over the patterning device in a given referencedirection (the “scanning” direction) while synchronously moving thesubstrate parallel or anti-parallel to this reference direction.Different portions of the pattern on the patterning device aretransferred to one target portion progressively. Since, in general, thelithographic projection apparatus will have a reduction ratio M (e.g.,4), the speed F at which the substrate is moved will be 1/M times thatat which the projection beam scans the patterning device. Moreinformation with regard to lithographic devices can be found in, forexample, U.S. Pat. No. 6,046,792, incorporated herein by reference.

Prior to transferring the pattern from the patterning device to thesubstrate, the substrate may undergo various procedures, such aspriming, resist coating and a soft bake. After exposure, the substratemay be subjected to other procedures (“post-exposure procedures”), suchas a post-exposure bake (PEB), development, a hard bake andmeasurement/inspection of the transferred pattern. This array ofprocedures is used as a basis to make an individual layer of a device,e.g., an IC. The substrate may then undergo various processes such asetching, ion-implantation (doping), metallization, oxidation,chemo-mechanical polishing, etc., all intended to finish off theindividual layer of the device. If several layers are required in thedevice, then the whole procedure, or a variant thereof, is repeated foreach layer. Eventually, a device will be present in each target portionon the substrate. These devices are then separated from one another by atechnique such as dicing or sawing, whence the individual devices can bemounted on a carrier, connected to pins, etc.

Thus, manufacturing devices, such as semiconductor devices, typicallyinvolve processing a substrate (e.g., a semiconductor wafer) using anumber of fabrication processes to form various features and multiplelayers of the devices. Such layers and features are typicallymanufactured and processed using, e.g., deposition, lithography, etch,chemical-mechanical polishing, and ion implantation. Multiple devicesmay be fabricated on a plurality of dies on a substrate and thenseparated into individual devices. This device manufacturing process maybe considered a patterning process. A patterning process involves apatterning step, such as optical and/or nanoimprint lithography using apatterning device in a lithographic apparatus, to transfer a pattern onthe patterning device to a substrate and typically, but optionally,involves one or more related pattern processing steps, such as resistdevelopment by a development apparatus, baking of the substrate using abake tool, etching using the pattern using an etch apparatus, etc.

As noted, lithography is a central step in the manufacturing of devicesuch as ICs, where patterns formed on substrates define functionalelements of the devices, such as microprocessors, memory chips, etc.Similar lithographic techniques are also used in the formation of flatpanel displays, micro-electro mechanical systems (MEMS) and otherdevices.

As semiconductor manufacturing processes continue to advance, thedimensions of functional elements have continually been reduced whilethe amount of functional elements, such as transistors, per device hasbeen steadily increasing over decades, following a trend commonlyreferred to as “Moore's law.” At the current state of technology, layersof devices are manufactured using lithographic projection apparatusesthat project a design layout onto a substrate using illumination from adeep-ultraviolet illumination source, creating individual functionalelements having dimensions well below 100 nm, i.e. less than half thewavelength of the radiation from the illumination source (e.g., a 193 nmillumination source).

This process in which features with dimensions smaller than theclassical resolution limit of a lithographic projection apparatus areprinted, is commonly known as low-k1 lithography, according to theresolution formula CD=k1×λ/NA, where λ is the wavelength of radiationemployed (currently in most cases 248 nm or 193 nm), NA is the numericalaperture of projection optics in the lithographic projection apparatus,CD is the “critical dimension”—generally the smallest feature sizeprinted—and k1 is an empirical resolution factor. In general, thesmaller k1 the more difficult it becomes to reproduce a pattern on thesubstrate that resembles the shape and dimensions planned by a designerin order to achieve particular electrical functionality and performance.To overcome these difficulties, sophisticated fine-tuning steps areapplied to the lithographic projection apparatus, the design layout, orthe patterning device. These include, for example, but not limited to,optimization of NA and optical coherence settings, customizedillumination schemes, use of phase shifting patterning devices, opticalproximity correction (OPC, sometimes also referred to as “optical andprocess correction”) in the design layout, or other methods generallydefined as “resolution enhancement techniques” (RET).

The term “projection optics,” as used herein, should be broadlyinterpreted as encompassing various types of optical systems, includingrefractive optics, reflective optics, apertures and catadioptric optics,for example. The term “projection optics” may also include componentsoperating according to any of these design types for directing, shapingor controlling the projection beam of radiation, collectively orsingularly. The term “projection optics” may include any opticalcomponent in the lithographic projection apparatus, no matter where theoptical component is located on an optical path of the lithographicprojection apparatus. Projection optics may include optical componentsfor shaping, adjusting and/or projecting radiation from the sourcebefore the radiation passes the patterning device, and/or opticalcomponents for shaping, adjusting and/or projecting the radiation afterthe radiation passes the patterning device. The projection opticsgenerally exclude the source and the patterning device.

SUMMARY

A method for training a machine learning model to generate acharacteristic pattern includes obtaining training data associated witha reference feature in a reference image, wherein the training dataincludes (i) location data of each portion of a plurality of portions ofthe reference feature, and (ii) a presence value indicating whether theportion of the reference feature is located within a reference assistfeature generated for the reference feature; and training, based on thetraining data associated with the reference feature, the machinelearning model such that a metric between a predicted presence value andthe presence value is minimized

In some embodiments, the characteristic pattern is used formanufacturing a mask pattern, which is further used for printing atarget pattern on a substrate.

In some embodiments, the reference image is a continuous transmissionmask (CTM) image generated by simulating an optical proximity correctionprocess using the target pattern, and the reference feature correspondsto a target feature from the target pattern.

In some embodiments, the reference assist feature includessub-resolution assist features placed around the reference feature, andthe sub-resolution assist features are rectilinear in shape.

In some embodiments, the training data includes training data for aplurality of reference features in one or more reference images.

Furthermore, the method of training the machine learning model includes(a) executing, the machine learning model using the training data, tooutput the predicted presence value associated with the correspondingportion of the reference feature; (b) determining the metric between thepredicted presence value and the presence value; (c) adjusting themachine learning model such that the cost function is reduced; (d)determining whether the metric is minimized; and (e) responsive to notminimized, performing steps (a), (b), (c), and (d).

In some embodiments, the method further includes obtaining a specifiedreference image; and determining, via executing the machine learningmodel using the specified reference image, a preferred assist featurefor placement in relation to a specified feature of the specifiedreference image, wherein the specified feature corresponds to a targetfeature of a target pattern to be printed on the substrate.

In some embodiments, determining the preferred assist feature includesobtaining, from the specified reference image and using an intensitythreshold, a specified contour of the specified feature, generating askeleton of the specified contour, inputting location data and distancedata to the machine learning model, wherein the location data includescoordinates of a set of points on the skeleton, wherein the distancedata indicates a closest distance from a point of the set of points tothe specified contour, and obtaining, from the machine learning model, apredicted presence value for each point of the set of points, whereinthe predicted presence value indicates whether the corresponding pointis predicted to be located within the preferred assist feature, whereinthe set of points includes (a) a covered set of points that is predictedto located within the preferred assist feature, and (b) an uncovered setof points that is predicted not to be located within the preferredassist feature.

In some embodiments, the method of determining the preferred assistfeature further includes generating a plurality of assist feature setsto cover points from the covered set of points, determining a rewardvalue for each assist feature set using a scoring function, anddetermining a first assist feature set of the assist feature sets havinga highest reward value as the preferred assist feature for placement inrelation to the specified contour.

In some embodiments, the method of determining the reward value for eachassist feature set includes (i) selecting a point from the uncovered setof points as a cut-off point, wherein the cut-off point divides theskeleton into a plurality of segments, (ii) generating an assist featureset of the plurality of assist feature sets having a candidate assistfeature for each segment of the plurality of segments, wherein thecandidate assist feature is generated based on (a) the distance dataassociated with each point of the set of points, and (b) a set ofconstraints the candidate assist feature has to satisfy formanufacturing of the mask pattern, (iii) determining a reward valueassociated with the assist feature set as a function of (a) imageintensity value within the assist feature set, and (b) the intensitythreshold, and iterating through steps (i), (ii) and (iii) by selectinga different cut-off point from the uncovered set of points, generatinganother assist feature set, and determining their corresponding rewardvalue.

In some embodiments, the distance value indicates a closest distancefrom a point to the specified contour.

In some embodiments, the method further includes generating acharacteristic pattern with the preferred assist feature, wherein thecharacteristic pattern is a pixelated image that includes the preferredassist feature placed in relation to the specified feature.

In some embodiments, the method of generating the characteristic patternincludes generating the characteristic pattern with a plurality ofpreferred assist features, wherein the preferred assist features areplaced in relation to a plurality of reference features of the specifiedreference image, wherein the preferred assist features are determined byexecuting the machine learning model for the reference features.

In some embodiments, the method of generating the characteristic patternincludes adjusting the placement of the preferred assist featuresfurther based on a set of constraints related to manufacturing of themask pattern.

In some embodiments, the machine learning model is a sequence labelingmodel.

In some embodiments, the sequence labeling model includes aBidirectional Long Short-term Memory (BiLSTM) network.

Furthermore, in some embodiments, obtaining the training data includesgenerating a plurality of assist feature sets for the reference featurebased on a set of constraints for manufacturing of a mask pattern,wherein each assist feature set is associated with a reward value thatis determined based on a specified scoring function, determining aspecified assist feature set of the plurality of assist feature setsassociated with a highest reward value as the reference assist feature,determining a status value for each portion of the reference feature asa function of the reward value of the plurality of assist feature setsand a number of assist feature sets in which the corresponding portionis determined to be located within, and generating the location data andthe presence value of the training data for each portion of thereference feature, wherein the presence value is set to a first value ifthe status value of the corresponding portion satisfies a statusthreshold, the first value indicating that the corresponding portion islocated within the reference assist feature.

In some embodiments, the method of generating the presence valueincludes setting the presence value to a second value if the statusvalue of the corresponding portion does not satisfy the statusthreshold, the second value indicating that the corresponding portion isnot located within the reference assist feature.

In some embodiments, the method of generating the plurality of assistfeature sets includes generating a skeleton of the reference feature;selecting a plurality of cut-off points on the skeleton, wherein eachcut-off point segments the skeleton into a plurality of segments; andfor each cut-off point, generating an assist feature set having areference assist feature for each segment of the plurality of segments,wherein the assist feature set is generated based on the set ofconstraints and a distance value associated with each point of a set ofpoints on the skeleton.

In some embodiments, the method of determining the assist feature sethaving the highest reward value includes determining, using thespecified scoring function, the reward value of an assist feature set ofthe plurality of assist feature sets as a function of (a) imageintensity value within the assist feature set, and (b) an intensitythreshold.

In some embodiments, the intensity threshold is used to generate acontour of the reference feature, wherein the contour is used togenerate the skeleton of the reference feature.

In some embodiments, the method of determining the status value for eachportion of the reference feature includes determining the status valuefor each point on the skeleton.

In some embodiments, the method further includes determining the statusthreshold as a function of a maximum and/or minimum of the status valuesof the set of points on the skeleton.

In some embodiments, the method of generating the training data for eachportion of the reference feature includes generating the location dataand the presence value for each point on the skeleton of the referencefeature.

In a related aspect, a method for generating a characteristic patternincludes obtaining a contour of a reference feature from a referenceimage; executing, by a hardware computer system and using the contour, amachine learning model for determining a preferred assist feature set tobe placed around the contour, and wherein the preferred assist featureset has a reward value that is highest among reward values of aplurality of assist feature sets, and wherein the reward value iscalculated as a function of an intensity threshold used to generate thecontour; and generating the characteristic pattern with the contour andthe preferred assist feature set.

In some embodiments, the characteristic pattern is used formanufacturing a mask pattern that is used for printing a target patternon a substrate.

In some embodiments, the reference image is a CTM image.

In some embodiments, the method of executing the machine learning modelto determine the preferred assist feature set includes generating askeleton of the contour, wherein the skeleton includes a set of points;selecting a plurality of cut-off points on the skeleton, wherein eachcut-off point segments the skeleton into a plurality of segments; andfor each cut-off point, generating an assist feature set of theplurality of assist feature sets for each segment of the plurality ofsegments, wherein the assist feature set is generated based on a set ofconstraints and a distance value associated with each point on theskeleton.

In some embodiments, the method further includes determining the rewardvalue of an assist feature set as a function of (a) intensity valueassociated with each point of the skeleton that is located within theassist feature set, and (b) the intensity threshold; and selecting oneof the assist feature sets having a highest reward value as thepreferred assist feature set.

In some embodiments, the method further includes generating, using thepreferred assist feature set, training data for training a secondmachine learning model to generate second characteristic pattern based asecond reference image.

In some embodiments, the training data includes training data for aplurality of preferred assist feature sets generated for a plurality ofcontours from the reference image.

In some embodiments, the method of generating the training data includesgenerating coordinates of each point of the skeleton of the contour; andgenerating a presence value associated with each point of the skeleton,wherein the presence value indicates whether the corresponding point islocated within the preferred assist feature set.

In some embodiments, the method of generating the coordinates of eachpoint includes generating coordinates of a pixel corresponding to thepoint in the reference image.

In some embodiments, the method of generating the presence valueincludes determining a status value for each point of the skeleton as afunction of the reward value of the plurality of assist feature sets anda number of assist feature sets in which the corresponding point isdetermined to be located within; determining a status threshold as afunction of maximum status value and a minimum status value of the setof points of the skeleton; and generating the presence value for eachpoint of the skeleton, wherein the presence value is set to a firstvalue if the status value of the corresponding point satisfies thestatus threshold, the first value indicating that the correspondingpoint is located within the preferred assist feature set.

In some embodiments, the method further includes training, based on thetraining data, the second machine learning model such that a costfunction that determines a difference between a predicted presence valueand the presence value is minimized

In a related aspect, a method for generating a characteristic patternfor a mask pattern includes obtaining a reference image having referencefeatures; obtaining a contour of a reference feature of the referencefeatures from the reference image; generating a skeleton of the contour;determining, via executing a machine learning model using the skeleton,a presence value indicating whether each point of a set of points on theskeleton is located within a preferred assist feature set to begenerated for placement around the reference feature; and generating acharacteristic pattern using the presence value.

In some embodiments, the characteristic pattern is a pixelated imagethat includes the preferred assist feature set placed in relation to thecontour.

In some embodiments, the set of points includes (a) a covered set ofpoints that is predicted to located within the preferred assist featureset, and (b) an uncovered set of points that is predicted not to belocated within the preferred assist feature set.

In some embodiments, the method of generating the characteristic patternusing the presence value includes (i) selecting a point from theuncovered set of points as a cut-off point, wherein the cut-off pointdivides the skeleton into a plurality of segments; (ii) generating afirst assist feature set having an assist feature for each segment ofthe plurality of segments, wherein the assist feature is generated basedon (a) a distance value associated with each point of the set of points,and (b) a set of constraints the assist feature has to satisfy formanufacturing of the mask pattern; (iii) determining a reward valueassociated with the first assist feature set as a function of (a)intensity value associated with each point of the set of points locatedwithin the first assist feature set, and (b) an intensity threshold thatis used in obtaining the contour; iterating through steps (i), (ii) and(iii) by selecting a different cut-off point from the uncovered set ofpoints, generating another assist feature set, and determining theircorresponding reward value; and determining one of the assist featuresets that has a highest reward value as the preferred assist feature setfor placement in relation to the reference feature.

In some embodiments, the method of generating the first assist featureset includes performing a random perturbation on the first assistfeature set and applying the set of constraints to the first assistfeature set.

In some embodiments, the method of generating the characteristic patternincludes generating the characteristic pattern with a plurality ofpreferred assist feature sets for placement in relation to a pluralityof reference features from the reference image.

In some embodiments, the reference image is a CTM image

According to an embodiment, there is provided a computer program productcomprising a non-transitory computer readable medium having instructionsrecorded thereon. The instructions, when executed by a computer,implement the methods listed in the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this specification, show certain aspects of the subject matterdisclosed herein and, together with the description, help explain someof the principles associated with the disclosed embodiments. In thedrawings,

FIG. 1 illustrates a block diagram of various subsystems of alithographic projection apparatus, according to an embodiment.

FIG. 2 illustrates an exemplary flow chart for simulating lithography ina lithographic projection apparatus, according to an embodiment.

FIG. 3 shows a block diagram for generating a characteristic patternfrom a reference image, consistent with various embodiments.

FIG. 4 is a block diagram for generating a contour and skeleton for afeature, consistent with various embodiments.

FIG. 5 shows another skeletonized representation of contours, consistentwith various embodiments.

FIG. 6 is a block diagram for generation of a preferred subresolutionassist feature (SRAF) set for a contour, consistent with variousembodiments.

FIG. 7 is a block diagram for generation of a preferred SRAF set using atrained machine learning (ML) model, consistent with variousembodiments.

FIG. 8 is a block diagram for training a SRAF placement model to predictSRAF placement data, consistent with various embodiments.

FIG. 9A is a flow diagram of a process for generating a characteristicpattern using reinforcement learning (RL) method, consistent withvarious embodiments.

FIG. 9B is a flow diagram of a process for determining a preferred SRAFset for a contour using the RL method, consistent with variousembodiments.

FIG. 10 is a flow diagram of a process for training a machine learningmodel to predict SRAF placement data, consistent with variousembodiments.

FIG. 11A is a flow diagram of a process for generating a characteristicpattern using a presence value predicted by a ML model, consistent withvarious embodiments.

FIG. 11B is a flow diagram of a process 1175 for determining a preferredSRAF set based on a presence value predicted by an ML model, consistentwith various embodiments.

FIG. 12 is a block diagram of an example computer system, according toan embodiment.

FIG. 13 is a schematic diagram of a lithographic projection apparatus,according to an embodiment.

FIG. 14 is a schematic diagram of another lithographic projectionapparatus, according to an embodiment.

FIG. 15 is a detailed view of the lithographic projection apparatus,according to an embodiment.

FIG. 16 is a detailed view of the source collector module of thelithographic projection apparatus, according to an embodiment.

FIG. 17 schematically depicts an embodiment of an electron beaminspection apparatus, according to an embodiment.

FIG. 18 schematically illustrates a further embodiment of an inspectionapparatus, according to an embodiment.

FIG. 19 schematically depicts an example inspection apparatus andmetrology technique.

FIG. 20 schematically depicts an example inspection apparatus.

FIG. 21 illustrates the relationship between an illumination spot of aninspection apparatus and a metrology target.

DETAILED DESCRIPTION

Although specific reference may be made in this text to the manufactureof ICs, it should be explicitly understood that the description hereinhas many other possible applications. For example, it may be employed inthe manufacture of integrated optical systems, guidance and detectionpatterns for magnetic domain memories, liquid-crystal display panels,thin-film magnetic heads, etc. The skilled artisan will appreciate that,in the context of such alternative applications, any use of the terms“reticle”, “wafer” or “die” in this text should be considered asinterchangeable with the more general terms “mask”, “substrate” and“target portion”, respectively.

In the present document, the terms “radiation” and “beam” are used toencompass all types of electromagnetic radiation, including ultravioletradiation (e.g. with a wavelength of 365, 248, 193, 157 or 126 nm) andEUV (extreme ultra-violet radiation, e.g. having a wavelength in therange of about 5-100 nm).

The patterning device can comprise, or can form, one or more designlayouts. The design layout can be generated utilizing CAD(computer-aided design) programs, this process often being referred toas EDA (electronic design automation). Most CAD programs follow a set ofpredetermined design rules in order to create functional designlayouts/patterning devices. These rules are set by processing and designlimitations. For example, design rules define the space tolerancebetween devices (such as gates, capacitors, etc.) or interconnect lines,so as to ensure that the devices or lines do not interact with oneanother in an undesirable way. One or more of the design rulelimitations may be referred to as “critical dimension” (CD). A criticaldimension of a device can be defined as the smallest width of a line orhole or the smallest space between two lines or two holes.

Thus, the CD determines the overall size and density of the designeddevice. Of course, one of the goals in device fabrication is tofaithfully reproduce the original design intent on the substrate (viathe patterning device).

The term “mask” or “patterning device” as employed in this text may bebroadly interpreted as referring to a generic patterning device that canbe used to endow an incoming radiation beam with a patternedcross-section, corresponding to a pattern that is to be created in atarget portion of the substrate; the term “light valve” can also be usedin this context. Besides the classic mask (transmissive or reflective;binary, phase-shifting, hybrid, etc.), examples of other such patterningdevices include a programmable mirror array and a programmable LCDarray.

An example of a programmable mirror array can be a matrix-addressablesurface having a viscoelastic control layer and a reflective surface.The basic principle behind such an apparatus is that (for example)addressed areas of the reflective surface reflect incident radiation asdiffracted radiation, whereas unaddressed areas reflect incidentradiation as undiffracted radiation. Using an appropriate filter, thesaid undiffracted radiation can be filtered out of the reflected beam,leaving only the diffracted radiation behind; in this manner, the beambecomes patterned according to the addressing pattern of thematrix-addressable surface. The required matrix addressing can beperformed using suitable electronic means.

An example of a programmable LCD array is given in U.S. Pat. No.5,229,872, which is incorporated herein by reference.

FIG. 1 illustrates a block diagram of various subsystems of alithographic projection apparatus 10A, according to an embodiment. Majorcomponents are a radiation source 12A, which may be a deep-ultravioletexcimer laser source or other type of source including an extreme ultraviolet (EUV) source (as discussed above, the lithographic projectionapparatus itself need not have the radiation source), illuminationoptics which, e.g., define the partial coherence (denoted as sigma) andwhich may include optics 14A, 16Aa and 16Ab that shape radiation fromthe source 12A; a patterning device 18A; and transmission optics 16Acthat project an image of the patterning device pattern onto a substrateplane 22A. An adjustable filter or aperture 20A at the pupil plane ofthe projection optics may restrict the range of beam angles that impingeon the substrate plane 22A, where the largest possible angle defines thenumerical aperture of the projection optics NA=n sin(Θmax), wherein n isthe refractive index of the media between the substrate and the lastelement of the projection optics, and Θmax is the largest angle of thebeam exiting from the projection optics that can still impinge on thesubstrate plane 22A.

In a lithographic projection apparatus, a source provides illumination(i.e. radiation) to a patterning device and projection optics direct andshape the illumination, via the patterning device, onto a substrate. Theprojection optics may include at least some of the components 14A, 16Aa,16Ab and 16Ac. An aerial image (AI) is the radiation intensitydistribution at substrate level. A resist model can be used to calculatethe resist image from the aerial image, an example of which can be foundin U.S. Patent Application Publication No. US 2009-0157630, thedisclosure of which is hereby incorporated by reference in its entirety.The resist model is related only to properties of the resist layer(e.g., effects of chemical processes which occur during exposure,post-exposure bake (PEB) and development). Optical properties of thelithographic projection apparatus (e.g., properties of the illumination,the patterning device and the projection optics) dictate the aerialimage and can be defined in an optical model. Since the patterningdevice used in the lithographic projection apparatus can be changed, itis desirable to separate the optical properties of the patterning devicefrom the optical properties of the rest of the lithographic projectionapparatus including at least the source and the projection optics.Details of techniques and models used to transform a design layout intovarious lithographic images (e.g., an aerial image, a resist image,etc.), apply OPC using those techniques and models and evaluateperformance (e.g., in terms of process window) are described in U.S.Patent Application Publication Nos. US 2008-0301620, 2007-0050749,2007-0031745, 2008-0309897, 2010-0162197, and 2010-0180251, thedisclosure of each which is hereby incorporated by reference in itsentirety.

One aspect of understanding a lithographic process is understanding theinteraction of the radiation and the patterning device. Theelectromagnetic field of the radiation after the radiation passes thepatterning device may be determined from the electromagnetic field ofthe radiation before the radiation reaches the patterning device and afunction that characterizes the interaction. This function may bereferred to as the mask transmission function (which can be used todescribe the interaction by a transmissive patterning device and/or areflective patterning device).

The mask transmission function may have a variety of different forms.One form is binary. A binary mask transmission function has either oftwo values (e.g., zero and a positive constant) at any given location onthe patterning device. A mask transmission function in the binary formmay be referred to as a binary mask. Another form is continuous. Namely,the modulus of the transmittance (or reflectance) of the patterningdevice is a continuous function of the location on the patterningdevice. The phase of the transmittance (or reflectance) may also be acontinuous function of the location on the patterning device. A masktransmission function in the continuous form may be referred to as acontinuous tone mask or a continuous transmission mask (CTM). Forexample, the CTM may be represented as a pixelated image, where eachpixel may be assigned a value between 0 and 1 (e.g., 0.1, 0.2, 0.3,etc.) instead of binary value of either 0 or 1. In an embodiment, CTMmay be a pixelated gray scale image, where each pixel having values(e.g., within a range [-255, 255], normalized values within a range [0,1] or [-1, 1] or other appropriate ranges).

The thin-mask approximation, also called the Kirchhoff boundarycondition, is widely used to simplify the determination of theinteraction of the radiation and the patterning device. The thin-maskapproximation assumes that the thickness of the structures on thepatterning device is very small compared with the wavelength and thatthe widths of the structures on the mask are very large compared withthe wavelength. Therefore, the thin-mask approximation assumes theelectromagnetic field after the patterning device is the multiplicationof the incident electromagnetic field with the mask transmissionfunction. However, as lithographic processes use radiation of shorterand shorter wavelengths, and the structures on the patterning devicebecome smaller and smaller, the assumption of the thin-maskapproximation can break down. For example, interaction of the radiationwith the structures (e.g., edges between the top surface and a sidewall)because of their finite thicknesses (“mask 3D effect” or “M3D”) maybecome significant. Encompassing this scattering in the masktransmission function may enable the mask transmission function tobetter capture the interaction of the radiation with the patterningdevice. A mask transmission function under the thin-mask approximationmay be referred to as a thin-mask transmission function. A masktransmission function encompassing M3D may be referred to as a M3D masktransmission function.

According to an embodiment of the present disclosure, one or more imagesmay be generated. The images includes various types of signal that maybe characterized by pixel values or intensity values of each pixel.Depending on the relative values of the pixel within the image, thesignal may be referred as, for example, a weak signal or a strongsignal, as may be understood by a person of ordinary skill in the art.The term “strong” and “weak” are relative terms based on intensityvalues of pixels within an image and specific values of intensity maynot limit scope of the present disclosure. In an embodiment, the strongand weak signal may be identified based on a selected threshold value.In an embodiment, the threshold value may be fixed (e.g., a midpoint ofa highest intensity and a lowest intensity of pixel within the image. Inan embodiment, a strong signal may refer to a signal with values greaterthan or equal to an average signal value across the image and a weaksignal may refer to signal with values less than the average signalvalue. In an embodiment, the relative intensity value may be based onpercentage. For example, the weak signal may be signal having intensityless than 50% of the highest intensity of the pixel (e.g., pixelscorresponding to target pattern may be considered pixels with highestintensity) within the image. Furthermore, each pixel within an image mayconsidered as a variable. According to the present embodiment,derivatives or partial derivative may be determined with respect to eachpixel within the image and the values of each pixel may be determined ormodified according to a cost function-based evaluation and/or gradientbased computation of the cost function. For example, a CTM image mayinclude pixels, where each pixel is a variable that can take any realvalue.

FIG. 2 illustrates an exemplary flow chart for simulating lithography ina lithographic projection apparatus, according to an embodiment. Sourcemodel 31 represents optical characteristics (including radiationintensity distribution and/or phase distribution) of the source.Projection optics model 32 represents optical characteristics (includingchanges to the radiation intensity distribution and/or the phasedistribution caused by the projection optics) of the projection optics.Design layout model 35 represents optical characteristics of a designlayout (including changes to the radiation intensity distribution and/orthe phase distribution caused by design layout), which is therepresentation of an arrangement of features on or formed by apatterning device. Aerial image 36 can be simulated from design layoutmodel 35, projection optics model 32, and design layout model 35. Resistimage 38 can be simulated from aerial image 36 using resist model 37.Simulation of lithography can, for example, predict contours and CDs inthe resist image.

More specifically, it is noted that source model 31 can represent theoptical characteristics of the source that include, but not limited to,numerical aperture settings, illumination sigma (σ) settings as well asany particular illumination shape (e.g. off-axis radiation sources suchas annular, quadrupole, dipole, etc.). Projection optics model 32 canrepresent the optical characteristics of the projection optics,including aberration, distortion, one or more refractive indexes, one ormore physical sizes, one or more physical dimensions, etc. Design layoutmodel 35 can represent one or more physical properties of a physicalpatterning device, as described, for example, in U.S. Pat. No.7,587,704, which is incorporated by reference in its entirety. Theobjective of the simulation is to accurately predict, for example, edgeplacement, aerial image intensity slope and/or CD, which can then becompared against an intended design. The intended design is generallydefined as a pre-OPC design layout which can be provided in astandardized digital file format such as GDSII or OASIS or other fileformat.

From this design layout, one or more portions may be identified, whichare referred to as “clips”. In an embodiment, a set of clips isextracted, which represents the complicated patterns in the designlayout (typically about 50 to 1000 clips, although any number of clipsmay be used). These patterns or clips represent small portions (i.e.circuits, cells or patterns) of the design and more specifically, theclips typically represent small portions for which particular attentionand/or verification is needed. In other words, clips may be the portionsof the design layout, or may be similar or have a similar behavior ofportions of the design layout, where one or more critical features areidentified either by experience (including clips provided by acustomer), by trial and error, or by running a full-chip simulation.Clips may contain one or more test patterns or gauge patterns.

An initial larger set of clips may be provided a priori by a customerbased on one or more known critical feature areas in a design layoutwhich require particular image optimization. Alternatively, in anotherembodiment, an initial larger set of clips may be extracted from theentire design layout by using some kind of automated (such as machinevision) or manual algorithm that identifies the one or more criticalfeature areas.

In a lithographic projection apparatus, as an example, a cost functionmay be expressed as

CF(z ₁ , z ₂ , . . . , z _(N))=Σ_(p=1) w _(p) f _(p) ²(z ₁ , z ₂ , . . ., z _(N))   (Eq. 1)

where (z₁, z₂, . . . , z_(N)) are N design variables or values thereof.f_(p)(z₁, Z₂, . . . , z_(N)) can be a function of the design variables(z₁, z₂, . . . , z_(N)) such as a difference between an actual value andan intended value of a characteristic for a set of values of the designvariables of (z₁, z₂, . . . , z_(N)). w_(p) is a weight constantassociated with f_(p)(z₁, z₂, , z_(N)). For example, the characteristicmay be a position of an edge of a pattern, measured at a given point onthe edge. Different f_(p)(z₁, z₂, . . . , z_(N)) may have differentweight w_(p). For example, if a particular edge has a narrow range ofpermitted positions, the weight w_(p) for the f_(p)(z₁, z₂, . . . ,z_(N)) representing the difference between the actual position and theintended position of the edge may be given a higher value. f_(p)(z₁, z₂,. . . , z_(N)) can also be a function of an interlayer characteristic,which is in turn a function of the design variables (z₁, z₂, . . . ,z_(N)). Of course, CF(z₁, z₂, . . . , z_(N)) is not limited to the formin Eq. 1. CF(z₁, z₂, . . . , z_(N)) can be in any other suitable form.

The cost function may represent any one or more suitable characteristicsof the lithographic projection apparatus, lithographic process or thesubstrate, for instance, focus, CD, image shift, image distortion, imagerotation, stochastic variation, throughput, local CD variation, processwindow, an interlayer characteristic, or a combination thereof. In oneembodiment, the design variables (z₁, Z₂, . . . , z_(N)) comprise one ormore selected from dose, global bias of the patterning device, and/orshape of illumination. Since it is the resist image that often dictatesthe pattern on a substrate, the cost function may include a functionthat represents one or more characteristics of the resist image. Forexample, f_(p)(z₁, z₂, . . . , z_(N)) can be simply a distance between apoint in the resist image to an intended position of that point (i.e.,edge placement error EPE_(p)(z₁, z₂, . . . , z_(N)). The designvariables can include any adjustable parameter such as an adjustableparameter of the source, the patterning device, the projection optics,dose, focus, etc.

The lithographic apparatus may include components collectively called a“wavefront manipulator” that can be used to adjust the shape of awavefront and intensity distribution and/or phase shift of a radiationbeam. In an embodiment, the lithographic apparatus can adjust awavefront and intensity distribution at any location along an opticalpath of the lithographic projection apparatus, such as before thepatterning device, near a pupil plane, near an image plane, and/or neara focal plane. The wavefront manipulator can be used to correct orcompensate for certain distortions of the wavefront and intensitydistribution and/or phase shift caused by, for example, the source, thepatterning device, temperature variation in the lithographic projectionapparatus, thermal expansion of components of the lithographicprojection apparatus, etc. Adjusting the wavefront and intensitydistribution and/or phase shift can change values of the characteristicsrepresented by the cost function. Such changes can be simulated from amodel or actually measured. The design variables can include parametersof the wavefront manipulator.

The design variables may have constraints, which can be expressed as(z₁, Z₂, . . . , z_(N)) E Z, where Z is a set of possible values of thedesign variables. One possible constraint on the design variables may beimposed by a desired throughput of the lithographic projectionapparatus. Without such a constraint imposed by the desired throughput,the optimization may yield a set of values of the design variables thatare unrealistic. For example, if the dose is a design variable, withoutsuch a constraint, the optimization may yield a dose value that makesthe throughput economically impossible. However, the usefulness ofconstraints should not be interpreted as a necessity. For example, thethroughput may be affected by the pupil fill ratio. For someillumination designs, a low pupil fill ratio may discard radiation,leading to lower throughput. Throughput may also be affected by theresist chemistry. Slower resist (e.g., a resist that requires higheramount of radiation to be properly exposed) leads to lower throughput.

As used herein, the term “patterning process” generally means a processthat creates an etched substrate by the application of specifiedpatterns of light as part of a lithography process. However, “patterningprocess” can also include plasma etching, as many of the featuresdescribed herein can provide benefits to forming printed patterns usingplasma processing.

As used herein, the term “target pattern” means an idealized patternthat is to be etched on a substrate.

As used herein, the term “printed pattern” means the physical pattern ona substrate that was etched based on a target pattern. The printedpattern can include, for example, troughs, channels, depressions, edges,or other two and three dimensional features resulting from a lithographyprocess.

As used herein, the term “process model” means a model that includes oneor more models that simulate a patterning process. For example, aprocess model can include an optical model (e.g., that models a lenssystem/projection system used to deliver light in a lithography processand may include modelling the final optical image of light that goesonto a photoresist), a resist model (e.g., that models physical effectsof the resist, such as chemical effects due to the light), and an OPCmodel (e.g., that can be used to make target patterns and may includescattering bars (SBARs) (also called as sub-resolution resist features(SRAFs)), etc.). As used herein, the term “calibrating” means to modify(e.g., improve or tune) and/or validate something, such as the processmodel.

In order to print a target pattern almost every feature of a designlayout of the target pattern has some modification so that a highfidelity of a projected image on the substrate to the target pattern isachieved. These modifications may include shifting or biasing of edgepositions or line widths as well as application of “assist” featuresthat are intended to assist projection of other features. The modifieddesign layout is then used to manufacture a patterning device (e.g., amask). A mask manufacturing has limitations related to a size, shape andpositioning of the features (e.g., assist features and main features).Hence, the modified design layout should be modified with certainmanufacturing limitations in mind as well.

Currently, one of the most accurate mask design methods for generatingassist features such as SRAFs is the CTM method. The CTM method firstdesigns a grayscale mask, referred to as a continuous transmission map,or CTM. The method involves optimization of grey scale values using agradient descent, or other optimization methods so that a performancemetric (e.g., edge placement error (EPE)) of a lithographic apparatus isimproved. However, the CTM cannot be manufactured as a mask itself,since it is a grayscale mask with unmanufacturable features. The CTM isnonetheless viewed as an ideal model which is the basis for amanufacturable mask. After the CTM is optimized, a mask design processproceeds to a bar extraction process. An example CTM optimizationprocess is discussed in detail in U.S. patent publicationUS20170038692A1, which is incorporated herein in its entirety byreference, that describes different flows of optimization forlithographic processes.

In the bar extraction process, the CTM is used to guide the placement ofSRAFs. In an embodiment, the SRAFs may be curved, rectangular or othergeometric shape, where the shape is easy to manufacture, e.g., withe-beam lithography. After the bar extraction process, an edge-based OPCis conducted on the main features (e.g., a target feature of a targetpattern to be printed on the substrate) of the design layout. In theedge-based OPC, edges of the main features are adjusted to ensureaccurate printing of the target pattern on the substrate.

Current SRAF placement is based on a reference image (e.g., a CTM), andthe method includes: (a), deriving ridge lines on the reference image,(b) placing SRAFs along the ridge lines, and (c) applying mask rulecheck (MRC) constraints on the SRAFs. According to the definition ofridge, the generated ridge lines are sensitive to local intensitymaximum or minimum, and many ridge lines may cross same point. Thus, theridge-based SRAFs overlap a lot before applying MRC. The MRC cleanupstep becomes computationally intensive in performing the clean-up. Whenthe final SRAF is rasterized, the resulting image will be very differentfrom the original reference image the SRAF extraction is applied on.

The current bar extraction methods may use heuristics to guide a desiredplacement and size of SRAFs. These heuristics may not be accurate, andcomputationally intensive. The existing methods for SRAF generation mayrely on inexact heuristics that often have sub-optimal results, e.g., interms of process window or consistency. For example, sometimes verticalbars are placed where horizontal bars would be more natural and workbetter, or vice versa. When these sub-optimal SRAFs are included in amask pattern, which is further used in a lithographic apparatus, theresulting performance of the patterning process may not meet a desiredperformance criterion.

The methods of the present disclosure seek to optimize determination ofSRAF placements in generating a characteristic pattern. In someembodiments, the result will be a mask that is close to a CTM as well aseasy to manufacture.

The methods (e.g., related to FIGS. 6 and 8-10 , including method 1000)described herein train a machine learning model to determine a placementof SRAFs in generating a characteristic pattern. In some embodiments,the characteristic pattern is an extraction friendly map or image thatincludes features that are easy to extract. As an example, thecharacteristic pattern includes SRAFs and/or main features, whichcorrespond to target features of a target pattern to be printed on thesubstrate. The SRAFs may be rectilinear in shape. In another example, anSRAF may include a curved feature.

In an embodiment, the placement of the SRAFs in the characteristicpattern is determined from a machine learning model trained to closelyfollow a reference image (e.g., the CTM) as well as design rules relatedto manufacturing of the mask pattern. In an embodiment, a maskmanufactured using the characteristic pattern will improve a performanceof the patterning process (e.g., a process window). For example, alithographic apparatus can employ the mask for printing patterns on asubstrate. Such printed pattern will have minimum errors or result inhigh yield of the patterning process. In some embodiments, processwindow is a collection of values of process parameters that allowcircuit to be manufactured and to operate under desired specifications.For instance, as an example, lithographic process window is typicallydefined as the set of {focus, exposure} points to control CD variationto within a specified range.

In an embodiment, design rules used herein refer to limitation relatedto manufacturing of the mask, for example, mask rule check (MRC)constraints. In the present disclosure, the design rules herein may bedifferent from design rules (e.g., minimum CD, minimum pitch) associatedwith a design layout e.g., target patterns that need to be printed on asubstrate. For mask patterns, the design rules do not necessarily followdesign rules related to the design layout. For example, SRAFs can besmall and also violate minimum pitch requirement.

In an embodiment, for example, MRC may include parameters such as arelative position of a feature (e.g., SRAFs) with respect to neighboringfeatures, a position of an SRAF with respect to main feature or otherSRAFs, a shape and size of a feature, or a combination thereof. Forexample, the MRC constraint can be a feature having a rectilinear shape,a curved shape having a radius of curvature within a specified range, ora combination thereof. In an embodiment, the design rules may be definedbased on heuristics e.g., a user-experience and past printingperformance. The methods apply the MRC constraints in generating thecharacteristic pattern.

FIG. 3 shows a block diagram for generating a characteristic patternfrom a reference image, consistent with various embodiments. A generatormodule 350 accepts as input a reference image 305 and generates acharacteristic pattern 320 based on the reference image 305. Thecharacteristic pattern is used in manufacturing a mask pattern that maybe used in printing a target pattern on a substrate. In someembodiments, the reference image 305 is an image, such as a CTM or amask image, having features (e.g., main feature such as referencefeature 307). The main features correspond to target features of atarget pattern to be printed on the substrate. In some embodiments, theCTM is generated by performing one or more OPC related process on thetarget pattern. In some embodiments, the mask image may be predictedusing ML methods or generated using other known methods. The referenceimage 305 may be stored in a database 360. The database 360 can alsostore other information such as the characteristic pattern 320 and anyother data necessary to generate the characteristic pattern 320.

In some embodiments the characteristic pattern 320 is an image thatincludes main features and SRAFs in which the SRAFs are placed near themain features. For example, the characteristic pattern 320 includescontours of the main features (e.g., contour 310 of the referencefeature 307) and a preferred SRAF set 325 having one or more SRAFsplaced near the contour 310. In some embodiments, the characteristicpattern 320 is similar to the reference image 305 but is more extractionfriendly than the reference image 305 as the features fromcharacteristic pattern 320 are easy to extract, and a mask patternmanufactured using such an image improves the pattering process byminimizing the number of errors and/or improving a process window inprinting the target pattern on a substrate. In some embodiments, thecharacteristic pattern may be an image composed exclusively ofrectangles that represents an optimized mask design.

The generator module 350 can implement the methods in several differentcomputation or training flows (e.g., method 900 of FIG. 9A and 1100 ofFIG. 11A) to generate the characteristic pattern 320. Each of theseflows takes, as an input, a reference image 305 (e.g., a CTM, CTM+, or amachine learning (ML) predicted mask image (MI)). In the case of the CTMas input, the CTM may have already been optimized to print the desiredpattern. The output for each method is the characteristic pattern 320.

As an example, in a first method, an ML model such as reinforcementlearning (RL) method may be used in determining the characteristicpattern 320. In some embodiments, reinforcement learning is an area ofmachine learning concerned with how software agents ought to takeactions in an environment in order to maximize some notion of cumulativereward. Reinforcement learning is one of different types of basicmachine learning paradigms, alongside supervised learning andunsupervised learning. RL differs from supervised learning in notneeding labelled input/output pairs be presented, and in not needingsub-optimal actions to be explicitly corrected. Instead the focus is onfinding a balance between exploration (of uncharted territory) andexploitation (of current knowledge). RL collects information byinteracting with the system and getting a reward. In the RL method, anSRAF generator model 354 in the generator module 350 may obtain askeleton 315 of a contour 310, determine a status value for each pointin the skeleton 315 (referred to as “skeleton point”), select cut-offpoints on the skeleton 315 (e.g., randomly) to generate multiplesegments of the skeleton 315 based on the cut-off points, place an SRAFfor at least some of the segments to create a SRAF set, and calculatereward for the SRAF set. The above process (among other processes thatwill be described in the later paragraphs) can be repeated for variouscut-off points to generate various SRAF sets, and an SRAF set with areward value satisfying a criterion (e.g., SRAF set with the highestreward value) is chosen as a preferred SRAF set. Similarly, a preferredSRAF set is determined for each contour extracted from the referenceimage 305 and then a characteristic pattern 320 with the SRAFs placedbased on the preferred SRAF sets is generated. In some embodiments, theRL method can be implemented using Monte Carlo method, which usesrandomness for deterministic problems difficult to solve using otherapproaches. Additional details of the RL method are described at leastwith reference to FIGS. 6, 9A and 9B.

While the RL method determines the best placement of SRAFs, the RLmethod may have to be repeated for each of the contours as there is nolearning from one contour that may be used to generate a preferred SRAFset for another contour. Accordingly, in some embodiments, in a secondmethod, an ML model may be trained using supervised learning to generatethe characteristic pattern 320 (e.g., FIGS. 9 and 10 ).

As an example, the supervised learning method uses a neural network thatis trained on SRAF placement data associated with a set of referenceimages that is generated using one or more methods, including existingmethods or other ML based methods such as the RL method described above.Once trained, a reference image can be inserted as the input, and thetrained machine learning model generates a characteristic pattern. Forexample, from the preferred SRAF sets generated using the RL method,labeled SRAF placement data is created for each skeleton 315, whichcontains information such as whether each skeleton point is covered by(e.g., lies in or located within) the preferred SRAF set of that contourand skeleton distance information of the skeleton point (e.g., a leastdistance from the skeleton point to the contour). Such labeled datacreated for a number of skeletons (e.g., of contours from one or morereference images) is used as training data to train an ML model (e.g.,SRAF placement model 353) to predict whether, for an input skeleton,each skeleton point is to be covered by an SRAF set or not. Thepredicted data (also referred to as “SRF placement data”), whichcontains information about which skeleton points are to be covered by anSRAF set and which should not be are then used to generate the preferredSRAF set for the contour corresponding to the input skeleton (e.g.,using SRAF generator model 354 as described above). In some embodiments,the supervised ML model includes a sequence labeling model, such as aBidirectional Long Short-term Memory (BiLSTM) neural network. Thesequence labeling model can also be implemented using other ML models,such as convolutional neural network (CNN), a recurrent neural network(RNN), Conditional Random Field (CRF), or other ML models. Additionaldetails with respect to the supervised learning method are described atleast with reference to FIGS. 7, 8, 10 and 11 .

FIG. 4 is a block diagram for generating a contour and skeleton for afeature, consistent with various embodiments. The reference image 305 isinput to a contour extractor 351, which extracts contours of thefeatures from the reference image 305, to generate a contour image 405.The contour image 405 includes the contours, such as the contour 310,for various features. The contour extractor 351 can extract the contour310 from the reference image 305 using one of many image analysistechniques. For example, the contour extractor 351 can extract thecontour 310 based on a change in intensity of pixels in the referenceimage 305. A change in intensity, gradient, and the like, of pixels inan image can identify an edge (e.g., contour). For example, when thereference image 305 is expressed as a greyscale image, when the changeexceeds a greyscale threshold (e.g., an intensity above or below adefined value), this can identify an edge (i.e. contour 310). In someembodiments, the contour extractor 351 uses a specified intensitythreshold to extract the contours, such as the contour 310.

The contour image 405 is input to a skeletonizer 352 to generate askeletonized representation 410, which includes a skeleton for eachcontour from the contour image 405. As an example, the skeletonizedrepresentation 410 includes a skeleton 315 for the contour 310. In shapeanalysis, skeleton (or topological skeleton) of a shape is a thinversion of that shape that is equidistant to its boundaries. Theskeleton usually emphasizes geometrical and topological properties ofthe shape, such as its topology, length, direction, and width. Togetherwith the distance of its points (e.g., skeleton distance) to the shapeboundary, the skeleton can also serve as a representation of the shape(they contain all the information necessary to reconstruct the shape).In some embodiments, a skeleton is one-pixel wide representation of abinary object in an image, and can be generated using one of manyskeletonization methods. In some embodiments, skeletonization techniquesinclude (a) detecting ridges in distance map of the boundary points, (b)calculating the Voronoi diagram generated by the boundary points, and(c) the layer by layer erosion called thinning.

The skeleton 315 is made up of a number of points (referred to as“skeleton points”). Each skeleton point is associated with (a) locationdata, such as co-ordinates of the skeleton point in the skeletonizedrepresentation 410, and (b) a skeleton distance, which is the leastdistance from the skeleton point to the contour. While a skeletonizedrepresentation includes skeletons of a number of contours from thereference image 305, a skeleton 315 for only one contour is shown in theskeletonized representation 410 for the sake of simplicity. FIG. 5 showsanother skeletonized representation of contours, consistent with variousembodiments. The skeletonized representation 505 includes a number ofcontours and their skeletons.

FIG. 6 is a block diagram for generation of a preferred SRAF set for acontour, consistent with various embodiments. In some embodiments, theSRAF generator model 354 uses the RL method (e.g., Monte Carlo method)to determine a preferred SRAF set 325 for the contour 310. The followingparagraphs describe the SRAF generator model 354 determining thepreferred SRAF set 325 with reference to one contour, e.g., contour 310.However, the SRAF generator model 354 may perform the same for othercontours (e.g., each contour in the skeletonized representation 410) todetermine a preferred SRAF set for the other contours in theskeletonized representation 410.

The skeletonized representation 410 is input to the SRAF generator model354 and the SRAF generator model 354 processes the skeleton 315 todetermine the preferred SRAF set 325 for the contour 310. The SRAFgenerator model assigns the following values to each of the skeletonpoints on the skeleton 315. These values are initialized to “0.”

-   -   R(i): Total Reward    -   N(i): Total Covered Times    -   S(i): Status Value

The SRAF generator model 354 selects one or more cut-off points on theskeleton 315 that divides the skeleton 315 into two or more segments,and determines an SRAF for each segment using the skeleton distance andMRC constraints, thus generating an SRAF set having multiple SRAFs. Forexample, a first cut-off point 606 is selected, which divides theskeleton 315 into two segments, and an SRAF is generated for each of thesegments, e.g., a first SRAF 607 and a second SRAF 608, forming a firstSRAF set 605.

The SRAF generator model 354 then performs a random perturbation processand an MRC clean process on the first SRAF set 605 to make the firstSRAF set 605 compliant with manufacturing standards of a mask pattern.In some embodiments, random perturbation is a process that slightlyoffsets the image, or mirrors the image horizontally or vertically. Oneof the reasons random perturbation is performed is to reduce overfittingthe ML model. As described above, the MRC clean is a process of applyingMRC constraints on the SRAFs to ensure that the characteristic patterngenerated with these SRAF sets is compliant with manufacturing standardsof a mask pattern.

The SRAF generator model 354 determines a reward value of the first SRAFset 605 using a scoring function. The scoring function uses imageintensity and an intensity threshold that is used to extract the contouras parameters for determining the reward value. An example scoringfunction for determining the reward value, r, is as follows:

$r = {\sum\limits_{{({x,y})}in{sraf}{set}}{f\left( {{I\left( {x,y} \right)} - {threshold}} \right)}}$

-   -   where threshold: threshold used to extract the contour (e. g. ,        intensity threshold)

$\begin{matrix}{{{f(x)}:{f(x)}} = \left\{ {{\begin{matrix}x & {x \geq 0} \\{ax} & {x < 0}\end{matrix}{and}a} = 0.1} \right.} & \end{matrix}$

-   -   I(x, y): Image Intensity of the reference image 305 at        coordinates (x,y) in the SRAF set

The SRAF generator model 354 updates the status value, S, of theskeleton points using the following algorithm:

for each skeleton points do { if skeleton point covered by (lies in orlocated within) an SRAF:  N(i) = N(i) + 1  R(i) = R(i) + r  S(i) =R(i)/N(i) } /* skeleton points loop */

-   -   where i is the index of skeleton point.

The above steps (e.g., beginning from selecting the cut-off points toupdating the status value) may be considered as iteration “A” and theiteration “A” is repeated by selecting different cut-off points (e.g.,random selection) to generate another SRAF set. For example, the SRAFgenerator model 354 repeats the iteration “A” by selecting a secondcut-off point 611 to generate a second SRAF set 610. The reward valuefor the second SRAF set 610 is determined and the status values of theskeleton points are further updated. Note that the status value of theskeleton points is not reset to “0” after generating the first SRAF set605. The SRAF generator model 354 repeats the iteration “A” a predefinednumber of times (e.g., one thousand or another number) by selectingdifferent cut-off points every iteration and generating an SRAF set ineach iteration “A” to generate “n” number of SRAF sets.

After generating “n” SRAF sets, the SRAF generator model 354 determinesa threshold value for the status value (e.g., status threshold). Thestatus threshold can be determined using any number of functions. Forexample, the status threshold can be determined as an average of thestatus values of the skeleton points. In another example, the statusthreshold can be determined as a function of a highest and lowest statusvalues (e.g., lowest status value+specified percentage of the range,where range is difference between highest and lowest status value) ofthe skeleton points. After the status threshold is determined, the SRAFgenerator model 354 determines those of the skeleton points havingstatus values below the status threshold as the cut-off points (e.g.,skeleton points that are not to be covered by the SRAF set). Afterdetermining the cut-off points, the SRAF generator model 354 performs arandom perturbation process and an MRC clean process on the “n” SRAFsets to make the “n” SRAF sets compliant with manufacturing standards ofa mask pattern, calculate the reward of the SRAF sets and determine anSRAF set that has a reward satisfying a specified criterion (e.g.,highest among the SRAF sets) as a preferred SRAF set 325 for the contour310.

The SRAF generator model 354 may perform the above steps (e.g.,beginning from processing a skeleton of the contour to determining thepreferred SRAF set) for other contours (e.g., each of the contours) fromthe skeletonized representation 410 to generate preferred SRAF sets forthe other contours.

After the preferred SRAF sets are determined, the SRAF generator model354 can generate the characteristic pattern 320, which includes thecontours extracted from the reference image 305 and their preferred SRAFsets.

One of the disadvantages with the above RL method is that the abovemethod is model-free, which means that learning gained from determiningthe preferred SRAF set 325 and therefore, the above method may have tobe performed each time a new contour is processed, which can become timeconsuming and compute intensive. In some embodiments, SRAF placementdata can be generated from the preferred SRAF sets generated using theRL method, and can be used as training data to train an ML model, suchas the SRAF placement model 353, to predict SRAF placement data that canbe used in generating a preferred SRAF set for any contour. For example,based on the preferred SRAF set 325, SRAF placement data 620 can begenerated. The SRAF placement data 620 indicates for each skeleton pointon the skeleton 315, (a) location data 621 of the skeleton point, (b)skeleton distance information 622 of the skeleton point (e.g., a leastdistance from the skeleton point to the contour), and (c) a presencevalue 623 (e.g., a label) indicating whether the skeleton point iscovered by (e.g., is present in, lies in or located within) thepreferred SRAF set 325. The presence value 623 can be of any form, e.g.,“0” or “1,” where “0” may indicate that the skeleton point is notlocated, covered or present in the SRAFs of the preferred SRAF set 325and “1” may indicate that the skeleton point is located, covered orpresent in the SRAFs of the preferred SRAF set 325. The SRAF placementdata 620 generated from the preferred SRAF set 325 can be used astraining data to train the SRAF placement model 353. Such SRAF placementdata is created for a number of skeletons (e.g., of contours from one ormore reference images) and are used to train the SRAF placement model353 to predict which skeleton points are to be covered by an SRAF set.Additional details with respect to training the SRAF placement model 353is discussed at least with reference to FIGS. 8 and 10 below.

FIG. 7 is a block diagram for generation of a preferred SRAF set using atrained ML model, consistent with various embodiments. The SRAFplacement model 353 is trained to predict SRAF placement data, whichindicates which skeleton points are to be covered by an SRAF set, forany given contour. In some embodiments, the SRAF placement model 353 isa sequence labeling model, such as BiLSTM network.

A skeletonized representation having a skeleton of a contour, such asthe skeletonized representation 410 having the skeleton 315 of thecontour 310, is input to the SRAF placement model 353. The skeletonizedrepresentation 410 is generated from the contour image 405, which isgenerated from the reference image 305, as described at least withreference to FIG. 4 above.

The SRAF placement model 353 processes the skeleton 315 to predict theSRAF placement data 316, which contains information about which skeletonpoints of the skeleton 315 are to be covered and which should not becovered by a preferred SRAF set. For example, the SRAF placement data316 can include the location data (e.g., x,y) coordinates of a skeletonpoint, and a presence value (e.g., “0” or “1”) indicating whether theskeleton point is to be covered (e.g., presence value “1”) or notcovered (e.g., presence value “0”) for each skeleton point. That is, theSRAF placement data 316 includes a covered set of points, which are theskeleton points to be covered by the preferred SRAF set, and anuncovered set of points, which are the skeleton points not to be coveredby the preferred SRAF set.

The predicted SRAF placement data 316 is then input to the SRAFgenerator model 354, which can determine the preferred SRAF set 325 forthe contour 310 as described at least with reference to FIG. 6 . Forexample, the SRAF generator model 354 selects one or more points fromthe uncovered set of points as cut-off points and then performsiteration “A” described at least with reference to FIG. 6 to generate anSRAF set and determine its reward. Then, the SRAF generator model 354repeats the iteration “A” a predefined number of times by selecting adifferent cut-off point from the uncovered set of points and generateanother SRAF set each time resulting in the generation of “n” number ofSRAF sets, where “n” is the predefined number of times iteration A isperformed. After generating “n” SRAF sets, the SRAF generator model 354determines an SRAF set that has a reward satisfying a specifiedcriterion (e.g., highest among the SRAF sets) as the preferred SRAF set325 for the contour 310.

Similarly, a preferred SRAF set is determined for each of the contoursfrom the reference image 305. The SRAF generator model 354 generates thecharacteristic pattern 320 based on the determined preferred SRAF sets.

FIG. 8 is a block diagram for training a SRAF placement model to predictSRAF placement data, consistent with various embodiments. As mentionedabove, in some embodiments, the SRAF placement model 353 is implementedusing a sequence labeling model, such as a BiLSTM neural network. Arecurrent neural network (RNN) is a class of artificial neural networkswhere connections between nodes form a directed graph along a temporalsequence. The RNN is typically used for sequential input/outputlearning. Long short-term memory (LSTM) is a special RNN, capable oflearning both short and long term dependencies, and it includes thefollowing components: cell (memory)—is responsible for keeping track ofthe dependencies between the elements in the input sequence; inputgate—controls the extent to which a new value flows into the cell;forget gate—controls the extent to which a value remains in the cell,and the output gate—controls the extent to which the value in the cellis used to compute the output activation of the LSTM unit. Theactivation function of the LSTM gates is often the logistic sigmoidfunction. In problems where all time steps of the input sequence areavailable, Bidirectional LSTMs train two instead of one recurrentnetwork. The first is trained on the input sequence as-is, and thesecond on a time-reversed copy of the input sequence. This can provideadditional context to the network and hopefully increase the accuracy ofthe network.

The SRAF placement model 353 is trained using training data, e.g., SRAFplacement data 620 generated in the RL method as described at least withreference to FIG. 6 . The training data includes SRAF placement data 620for a skeleton, which indicates for each skeleton point on the skeleton,(a) location data 621 of the skeleton point (e.g., co-ordinates of theskeleton point in the skeletonized representation 410), (b) skeletondistance information 622 of the skeleton point (e.g., a least distancefrom the skeleton point to the contour), and (c) a presence value 623indicating whether the skeleton point is covered by (e.g., is presentin, lies in or located within) a preferred SRAF set. The presence value623 can be of any form, e.g., “0” or “1,” where “0” may indicate thatthe skeleton point is not located, covered or present in the SRAFs ofthe preferred SRAF set and “1” may indicate that the skeleton point islocated, covered or present in the SRAFs of the preferred SRAF set.

The training is an iterative process and an iteration includes:inputting the SRAF placement data 620 to the SRAF placement model 353 togenerate a predicted presence value 805 for each of the skeleton points(e.g., indicating whether a skeleton point is predicted to be covered bya preferred SRAF set or not), determining a metric or cost functionassociated with the predicted presence value 805 and the actual presencevalue (e.g., a difference between the predicted presence value 805 andthe actual presence value from SRAF placement data 620), and adjustingthe model parameters to minimize the metric. As an example, the modelparameters are adjusted to reduce the difference. The training of theSRAF placement model 353 is continued by performing a number ofiterations with additional SRAF placement data until a specifiedcondition is satisfied (e.g., the metric is minimized or below a firstthreshold, and/or the rate at which the metric minimizes is less than asecond threshold). Once the specified condition is satisfied, the SRAFplacement model 353 is considered to be trained, and the trained SRAFplacement model 353 can be used to predict the SRAF placement data forany contour (e.g., new or unseen contour, which is a contour notpreviously processed by the SRAF placement model 353). An example ofpredicting the SRAF placement data using the trained SRAF placementmodel 353 is described at least with reference to FIG. 7 above.

FIG. 9A is a flow diagram of a process 900 for generating acharacteristic pattern using RL method, consistent with variousembodiments.

At operation 910, a contour 310 of a reference feature 307 (e.g.,feature that corresponds to a target feature from a target pattern to beprinted on the substrate) is obtained from a reference image 305. Insome embodiments, the reference image 305 is a CTM and is obtained fromthe database 360. A contour is extracted from the reference image 305(e.g., using intensity threshold) as described at least with referenceto FIG. 4 .

At operation 920, the SRAF generator model 354 is executed to determinea preferred SRAF set 325 to be placed near the contour 310. In someembodiments, the preferred SRAF set 325 has a reward value thatsatisfies a specified condition (e.g., highest of all the SRAF setsgenerated for the contour 310). The reward value is determined as afunction of intensity threshold value, e.g., as described at least withreference to FIG. 6 . In some embodiments, the SRAF generator model 354uses the RL method (e.g., Monte Carlo method) to determine the preferredSRAF set 325. In some embodiments, the SRAF generator model 354 invokesthe operations described at least with reference to FIG. 9B to determinethe preferred SRAF set for a contour. The SRAF generator model 354provides a contour as input to the operations of FIG. 9B and receivesthe preferred SRAF set from those operations.

The operations 910 and 920 are repeated for other contours (e.g., eachcontour) in the reference image 305 to determine the preferred SRAF setsfor the other contours.

At operation 930, the SRAF generator model 354 generates acharacteristic pattern 320, which is an extraction friendly image thathas the contours of the reference features from the reference image 305and the preferred SRAF sets placed near the corresponding contours. Forexample, the SRAF generator model 354 generates the contour 310 with thepreferred SRAF set 325 placed near the contour 310. In some embodiments,the characteristic pattern 320 is used to manufacture a mask patternthat is used in printing a target pattern on the substrate.

FIG. 9B is a flow diagram of a process 950 for determining a preferredSRAF set for a contour using the RL method, consistent with variousembodiments. In some embodiments, the process 950 is performed as partof the operation 920 of process 900. At operation 921, a skeletonizer352 receives as input a contour (e.g., contour 310) from operation 920of process 900) and process the contour 310 to generate a skeleton 315of the contour 310. The skeletonizer 352 generates the skeleton 315using one of many image analysis techniques, e.g., as described at leastwith reference to FIG. 4 .

At operation 922, the SRAF generator model 354 assigns the followingparameters to each of the skeleton points on the skeleton 315 andinitializes their values to “0.”

-   -   R(i): Total Reward    -   N(i): Total Covered Times    -   S(i): Status Value

At operation 923, the SRAF generator model 354 selects one or morecut-off points on the skeleton 315, which divides the skeleton 315 intotwo or more segments. For example, a first cut-off point 606 isselected, which divides the skeleton 315 into two segments.

At operation 924, the SRAF generator model 354 determines an SRAF foreach segment, using the skeleton distance and MRC constraints. Forexample, for the two segments created by the first cut-off point 606,the SRAF generator model 354 generates a first SRAF 607 and a secondSRAF 608, forming a first SRAF set 605.

At operation 925, the SRAF generator model 354 performs a randomperturbation process and an MRC clean process on the first SRAF set 605to make the first SRAF set 605 compliant with manufacturing standards ofa mask pattern. In some embodiments, random perturbation is a processthat slightly offsets the image, or mirrors the image horizontally orvertically. One of the reasons random perturbation is performed is toreduce overfitting the ML model. As described above, the MRC clean is aprocess of applying MRC constraints on the SRAFs to ensure that thecharacteristic pattern generated with these SRAF sets is compliant withmanufacturing standards of a mask pattern.

At operation 926, the SRAF generator model 354 determines a reward valueof the first SRAF set 605 using a scoring function. The scoring functionuses image intensity and an intensity threshold that is used to extractthe contour as parameters for determining the reward value. An examplescoring function for determining the reward value, r, is as follows:

$r = {\sum\limits_{{({x,y})}in{sraf}{set}}{f\left( {{I\left( {x,y} \right)} - {threshold}} \right)}}$

-   -   where threshold: threshold used to extract the contour (e.g.,        intensity threshold)

${{f(x)}:{f(x)}} = \left\{ {{\begin{matrix}x & {x \geq 0} \\{ax} & {x < 0}\end{matrix}{and}a} = 0.1} \right.$

-   -   I(x, y): Image Intensity of the reference image 305 at        coordinates (x, y) in the SRAF set

At operation 927, the SRAF generator model 354 updates the status value,S, of the skeleton points using the following algorithm:

for each skeleton points do { if skeleton point covered by (lies in orlocated within) an SRAF:  N(i) = N(i) + 1  R(i) = R(i) + r  S(i) =R(i)/N(i) } /* skeleton points loop */

-   -   where i is the index of skeleton point.

The SRAF generator model 354 repeats the operations 923-927 a predefinednumber of times (e.g., one thousand times or another number) byselecting different cut-off points each time and generating an SRAF seteach time resulting in generation of “n” number of SRAF sets, wherein“n” is the predefined number of times. The reward value for each of theSRAF sets is determined and the status values of the skeleton points arefurther updated. Note that the status value of the skeleton points isnot reset to “0” each time the operations 923-927 are repeated.

At operation 928, the SRAF generator model 354 determines a thresholdvalue for the status value (e.g., status threshold). The statusthreshold can be determined using any number of functions (e.g., as anaverage of the status values of the skeleton points, and as a functionof a highest and lowest status values (e.g., lowest statusvalue+specified percentage of the range, where range is differencebetween highest and lowest status value)). After the status threshold isdetermined, the SRAF generator model 354 determines those of theskeleton points having a status value below the status threshold as thecut-off points (e.g., skeleton points that are not to be covered by theSRAF set). After determining the cut-off points, the SRAF generatormodel 354 performs the operations 925-927 to make the “n” SRAF setscompliant with manufacturing standards of a mask pattern and calculatethe updated reward value of the SRAF sets.

At operation 929, the SRAF generator model 354 determines an SRAF setthat has a reward satisfying a specified criterion (e.g., highest amongthe SRAF sets) as a preferred SRAF set 325 for the contour 310. Thepreferred SRAF set 325 is now returned to the operation 920 of FIG. 9A.

In some embodiments, at operation 929 b, the SRAF generator model 354generates SRAF placement data from the preferred SRAF sets, which can beused as training data to train an ML model, such as the SRAF placementmodel 353, to predict SRAF placement data that can be used in generatinga preferred SRAF set for any contour. For example, the SRAF generatormodel 354 generates SRAF placement data 620 based on the preferred SRAFset 325. The SRAF placement data 620 indicates for each skeleton pointon the skeleton 315, (a) location data of the skeleton point, (b)skeleton distance information of the skeleton point (e.g., a leastdistance from the skeleton point to the contour), and (c) a presencevalue (e.g., label) indicating whether the skeleton point is covered by(e.g., is present in, lies in or located within) the preferred SRAF set325. The presence value can be of any form, e.g., “0” or “1,” where “0”may indicate that the skeleton point is not located, covered or presentin the SRAFs of the preferred SRAF set 325 and “1” may indicate that theskeleton point is located, covered or present in the SRAFs of thepreferred SRAF set 325. Such SRAF placement data is created for a numberof skeletons (e.g., of contours from one or more reference images) andare used to train the SRAF placement model 353 to predict which skeletonpoints are to be covered by an SRAF set.

Note that the operation 929 b, which is used to generate training data,is optional and not required to determine the preferred SRAF set usingthe RL method.

FIG. 10 is a flow diagram of a process 1000 for training a machinelearning model to predict SRAF placement data, consistent with variousembodiments. As mentioned above, in some embodiments, the SRAF placementmodel 353 is implemented using BiLSTM neural network.

At operation 1010, training data associated with a reference feature 307in a reference image 305 is obtained, e.g., from database 360. Thetraining data is used to train the SRAF placement model 353 to predictSRAF placement data that can be used in determining a preferred SRAF setfor a contour is obtained. The training data includes (i) location dataof each portion of a plurality of portions of the reference feature 307,and (iii) a presence value 623 indicating whether the portion of thereference feature 307 is located within a reference assist featuregenerated for the reference feature 307. For example, the training dataincludes SRAF placement data 620 for a skeleton 315 generated from thecontour 310 of the reference feature 307. The SRAF placement data 620for the skeleton 315 indicates for each skeleton point on the skeleton:(a) location data 621 of the skeleton point on the skeleton 315, (b)skeleton distance information 622 of the skeleton point (e.g., leastdistance from the skeleton point to the contour), and (c) a presencevalue 623 indicating whether the skeleton point is covered by (e.g., ispresent in, lies in or located within) a preferred SRAF set 325. Thepresence value 623 can be of any form, e.g., “0” or “1,” where “0” mayindicate that the skeleton point is not located, covered or present inthe SRAFs of the preferred SRAF set and “1” may indicate that theskeleton point is located, covered or present in the SRAFs of thepreferred SRAF set 325. In some embodiments, the training data isgenerated by the SRAF generator model 354 using the RL method asdescribed at least with reference to FIG. 6 and operation 929 b of FIG.9 . In some embodiments, the training data includes SRAF placement datafor a number of skeletons.

At operation 1020, the SRAF placement model 353 is trained using thetraining data associated with the reference feature 307 such that ametric between a predicted presence value 805 and the presence value 623is minimized The training is an iterative process and an iterationincludes: inputting the training data (e.g., SRAF placement data 620) tothe SRAF placement model 353 to generate a predicted presence value 805for each of the skeleton points (e.g., skeleton points of the skeleton315), which indicates whether a skeleton point is predicted to becovered by a preferred SRAF set or not, determining a metric associatedwith the predicted presence value 805 and the actual presence value(e.g., a difference between the predicted presence value 805 and theactual presence value from SRAF placement data 620), and adjusting themodel parameters to minimize the metric.

As an example, the model parameters are adjusted to reduce thedifference. The training of the SRAF placement model 353 is continued byperforming a number of iterations with additional SRAF placement datauntil a specified condition is satisfied (e.g., the metric is minimizedor below a first threshold, and/or the rate at which the metricminimizes is less than a second threshold).

Once the specified condition is satisfied, the SRAF placement model 353is considered to be trained, and the trained SRAF placement model 353can be used to predict the SRAF placement data for any contour (e.g.,new or unseen contour, which is a contour not previously processed bythe SRAF placement model 353). An example of predicting the SRAFplacement data using the trained SRAF placement model 353 is describedat least with reference to FIG. 7 above and FIG. 11 below.

FIG. 11A is a flow diagram of a process 1100 for generating acharacteristic pattern using a presence value predicted by a ML model,consistent with various embodiments. In some embodiments, the ML model,such as the SRAF placement model 353, is trained to predict a presencevalue that indicates which skeleton points of a skeleton are to becovered and which skeleton points are not be covered by a preferred SRAFset for a contour. The training is performed as described at least withreference to FIGS. 8 and 10 above. The following operations areperformed using the trained SRAF placement model 353.

At operation 1110, a reference image 305 is obtained, e.g., fromdatabase 360. In some embodiments, the reference image 305 is a CTM.

At operation 1120, a contour 310 of a reference feature 307 (e.g.,feature that corresponds to a target feature from a target pattern to beprinted on the substrate) is obtained from the reference image 305. Acontour is extracted from the reference image 305 (e.g., using intensitythreshold) as described at least with reference to FIG. 4 .

At operation 1130, a skeletonizer 352 processes the contour 310 togenerate a skeleton 315 of the contour 310. The skeletonizer 352generates the skeleton 315 using one of many image analysis techniques,e.g., as described at least with reference to FIG. 4 .

At operation 1140, the SRAF placement model 353 processes the skeleton315 to determine or generate the SRAF placement data 316, which containsa predicted presence value 805. For example, the SRAF placement data 316can include, for each skeleton point, the location data (e.g., x,y)coordinates of a skeleton point, and a predicted presence value 805(e.g., “0” or “1”) indicating whether the skeleton point is to becovered (e.g., presence value “1”) or not covered (e.g., presence value“0”). That is, the SRAF placement data 316 includes a covered set ofpoints, which are skeleton points that are to be covered by thepreferred SRAF set, and an uncovered set of points, which are skeletonpoints that are not to be covered by the preferred SRAF set.

At operation 1150, the SRAF generator model 354 generates acharacteristic pattern 320 based on the predicted presence value 805. Insome embodiments, the SRAF generator model 354 determines a preferredSRAF set for the contour 310 using the presence value 805 in theoperations described in FIG. 11B below. Similarly, preferred SRAF setsare determined for other contours in the reference image 305. After thepreferred SRAF sets are determined for the contours in the referenceimage 305, the SRAF generator model 354 generates the characteristicpattern 320 based on the preferred SRAF sets. In some embodiments, thecharacteristic pattern 320 is an extraction friendly image that has thecontours of the reference features from the reference image 305 andpreferred SRAF sets placed near the corresponding contours. In someembodiments, the characteristic pattern 320 is used to manufacture amask pattern that is used in printing a target pattern on the substrate.

FIG. 11B is a flow diagram of a process 1175 for determining a preferredSRAF set based on a presence value predicted by a ML model, consistentwith various embodiments. In some embodiments, the operations of process1175 are performed as part of operation 1150 of process 1100 of FIG. 11Aand are similar to some of the operations of the RL method discussed atleast with reference to process 950 of FIG. 9B. The process 1175receives as input SRAF placement data having a predicted presence valuefor a skeleton (e.g., SRAF placement data 316 having the predictedpresence value 805 for skeleton 315) and outputs a predicted SRAF forthe skeleton.

At operation 1151, the SRAF generator model 354 selects one or morepoints from the uncovered set of points in the SRAF placement data 316as cut-off points, which divides the skeleton 315 into multiplesegments.

At operation 1152, the SRAF generator model 354 performs an operationsimilar to the operation 924 of process 950 to determine an SRAF foreach segment, using the skeleton distance and MRC constraints. Forexample, for the two segments created by the first cut-off point 606,the SRAF generator model 354 generates a first SRAF 607 and a secondSRAF 608, forming a first SRAF set 605.

At operation 1153, the SRAF generator model 354 performs an operationsimilar to the operation 925 of process 950, which incldues performing arandom perturbation process and an MRC clean process on the first SRAFset 605 to make the first SRAF set 605 compliant with manufacturingstandards of a mask pattern.

At operation 1154, the SRAF generator model 354 performs an operationsimilar to the operation 926 of process 950 to determine a reward valueof the first SRAF set 605 using a scoring function.

At operation 1155, the SRAF generator model 354 performs an operationsimilar to the operation 927 to updates the status value, S, of theskeleton points.

At operation 1156, the SRAF generator model 354 performs an operationsimilar to the operation 929 to determine an SRAF set that has a rewardsatisfying a specified criterion (e.g., highest among the SRAF sets) asa preferred SRAF set 325 for the contour 310. The preferred SRAF set 325is now returned to the operation 1150 of process 1100.

FIG. 12 is a block diagram of an example computer system CS, accordingto an embodiment.

Computer system CS includes a bus BS or other communication mechanismfor communicating information, and a processor PRO (or multipleprocessor) coupled with bus BS for processing information. Computersystem CS also includes a main memory MM, such as a random access memory(RAM) or other dynamic storage device, coupled to bus BS for storinginformation and instructions to be executed by processor PRO. Mainmemory MM also may be used for storing temporary variables or otherintermediate information during execution of instructions to be executedby processor PRO. Computer system CS further includes a read only memory(ROM) ROM or other static storage device coupled to bus BS for storingstatic information and instructions for processor PRO. A storage deviceSD, such as a magnetic disk or optical disk, is provided and coupled tobus BS for storing information and instructions.

Computer system CS may be coupled via bus BS to a display DS, such as acathode ray tube (CRT) or flat panel or touch panel display fordisplaying information to a computer user. An input device ID, includingalphanumeric and other keys, is coupled to bus BS for communicatinginformation and command selections to processor PRO. Another type ofuser input device is cursor control CC, such as a mouse, a trackball, orcursor direction keys for communicating direction information andcommand selections to processor PRO and for controlling cursor movementon display DS. This input device typically has two degrees of freedom intwo axes, a first axis (e.g., x) and a second axis (e.g., y), thatallows the device to specify positions in a plane. A touch panel(screen) display may also be used as an input device.

According to one embodiment, portions of one or more methods describedherein may be performed by computer system CS in response to processorPRO executing one or more sequences of one or more instructionscontained in main memory MM. Such instructions may be read into mainmemory MM from another computer-readable medium, such as storage deviceSD. Execution of the sequences of instructions contained in main memoryMM causes processor PRO to perform the process steps described herein.One or more processors in a multi-processing arrangement may also beemployed to execute the sequences of instructions contained in mainmemory MM. In an alternative embodiment, hard-wired circuitry may beused in place of or in combination with software instructions. Thus, thedescription herein is not limited to any specific combination ofhardware circuitry and software.

The term “computer-readable medium” as used herein refers to any mediumthat participates in providing instructions to processor PRO forexecution. Such a medium may take many forms, including but not limitedto, non-volatile media, volatile media, and transmission media.Non-volatile media include, for example, optical or magnetic disks, suchas storage device SD. Volatile media include dynamic memory, such asmain memory MM. Transmission media include coaxial cables, copper wireand fiber optics, including the wires that comprise bus BS. Transmissionmedia can also take the form of acoustic or light waves, such as thosegenerated during radio frequency (RF) and infrared (IR) datacommunications. Computer-readable media can be non-transitory, forexample, a floppy disk, a flexible disk, hard disk, magnetic tape, anyother magnetic medium, a CD-ROM, DVD, any other optical medium, punchcards, paper tape, any other physical medium with patterns of holes, aRAM, a PROM, and EPROM, a FLASH-EPROM, any other memory chip orcartridge. Non-transitory computer readable media can have instructionsrecorded thereon. The instructions, when executed by a computer, canimplement any of the features described herein. Transitorycomputer-readable media can include a carrier wave or other propagatingelectromagnetic signal.

Various forms of computer readable media may be involved in carrying oneor more sequences of one or more instructions to processor PRO forexecution. For example, the instructions may initially be borne on amagnetic disk of a remote computer. The remote computer can load theinstructions into its dynamic memory and send the instructions over atelephone line using a modem.

A modem local to computer system CS can receive the data on thetelephone line and use an infrared transmitter to convert the data to aninfrared signal. An infrared detector coupled to bus BS can receive thedata carried in the infrared signal and place the data on bus BS. Bus BScarries the data to main memory MM, from which processor PRO retrievesand executes the instructions. The instructions received by main memoryMM may optionally be stored on storage device SD either before or afterexecution by processor PRO.

Computer system CS may also include a communication interface CI coupledto bus BS. Communication interface CI provides a two-way datacommunication coupling to a network link NDL that is connected to alocal network LAN. For example, communication interface CI may be anintegrated services digital network (ISDN) card or a modem to provide adata communication connection to a corresponding type of telephone line.As another example, communication interface CI may be a local areanetwork (LAN) card to provide a data communication connection to acompatible LAN. Wireless links may also be implemented. In any suchimplementation, communication interface CI sends and receiveselectrical, electromagnetic or optical signals that carry digital datastreams representing various types of information.

Network link NDL typically provides data communication through one ormore networks to other data devices. For example, network link NDL mayprovide a connection through local network LAN to a host computer HC.This can include data communication services provided through theworldwide packet data communication network, now commonly referred to asthe “Internet” INT. Local network LAN (Internet) both use electrical,electromagnetic or optical signals that carry digital data streams. Thesignals through the various networks and the signals on network datalink NDL and through communication interface CI, which carry the digitaldata to and from computer system CS, are exemplary forms of carrierwaves transporting the information.

Computer system CS can send messages and receive data, including programcode, through the network(s), network data link NDL, and communicationinterface CI. In the Internet example, host computer HC might transmit arequested code for an application program through Internet INT, networkdata link NDL, local network LAN and communication interface CI. Onesuch downloaded application may provide all or part of a methoddescribed herein, for example. The received code may be executed byprocessor PRO as it is received, and/or stored in storage device SD, orother non-volatile storage for later execution. In this manner, computersystem CS may obtain application code in the form of a carrier wave.

According to the present disclosure, the combination andsub-combinations of disclosed elements constitute separate embodiments.For example, the method for generating a predicted measured image andthe method for aligning a measured image with the predicted measuredimage may comprise separate embodiments, and/or these methods may beused together in the same embodiment.

FIG. 13 is a schematic diagram of a lithographic projection apparatus,according to an embodiment.

The lithographic projection apparatus can include an illumination systemIL, a first object table MT, a second object table WT, and a projectionsystem PS.

Illumination system IL, can condition a beam B of radiation. In thisparticular case, the illumination system also comprises a radiationsource SO.

First object table (e.g., patterning device table) MT can be providedwith a patterning device holder to hold a patterning device MA (e.g., areticle), and connected to a first positioner to accurately position thepatterning device with respect to item PS.

Second object table (substrate table) WT can be provided with asubstrate holder to hold a substrate W (e.g., a resist-coated siliconwafer), and connected to a second positioner to accurately position thesubstrate with respect to item PS.

Projection system (“lens”) PS (e.g., a refractive, catoptric orcatadioptric optical system) can image an irradiated portion of thepatterning device MA onto a target portion C (e.g., comprising one ormore dies) of the substrate W.

As depicted herein, the apparatus can be of a transmissive type (i.e.,has a transmissive patterning device). However, in general, it may alsobe of a reflective type, for example (with a reflective patterningdevice). The apparatus may employ a different kind of patterning deviceto classic mask; examples include a programmable mirror array or LCDmatrix.

The source SO (e.g., a mercury lamp or excimer laser, LPP (laserproduced plasma) EUV source) produces a beam of radiation. This beam isfed into an illumination system (illuminator) IL, either directly orafter having traversed conditioning means, such as a beam expander Ex,for example. The illuminator IL may comprise adjusting means AD forsetting the outer and/or inner radial extent (commonly referred to asσ-outer and σ-inner, respectively) of the intensity distribution in thebeam. In addition, it will generally comprise various other components,such as an integrator IN and a condenser CO. In this way, the beam Bimpinging on the patterning device MA has a desired uniformity andintensity distribution in its cross-section.

In some embodiments, source SO may be within the housing of thelithographic projection apparatus (as is often the case when source SOis a mercury lamp, for example), but that it may also be remote from thelithographic projection apparatus, the radiation beam that it producesbeing led into the apparatus (e.g., with the aid of suitable directingmirrors); this latter scenario can be the case when source SO is anexcimer laser (e.g., based on KrF, ArF or F2 lasing).

The beam PB can subsequently intercept patterning device MA, which isheld on a patterning device table MT. Having traversed patterning deviceMA, the beam B can pass through the lens PL, which focuses beam B ontotarget portion C of substrate W. With the aid of the second positioningmeans (and interferometric measuring means IF), the substrate table WTcan be moved accurately, e.g. so as to position different targetportions C in the path of beam PB. Similarly, the first positioningmeans can be used to accurately position patterning device MA withrespect to the path of beam B, e.g., after mechanical retrieval of thepatterning device MA from a patterning device library, or during a scan.In general, movement of the object tables MT, WT can be realized withthe aid of a long-stroke module (coarse positioning) and a short-strokemodule (fine positioning). However, in the case of a stepper (as opposedto a step-and-scan tool) patterning device table MT may just beconnected to a short stroke actuator, or may be fixed.

The depicted tool can be used in two different modes, step mode and scanmode. In step mode, patterning device table MT is kept essentiallystationary, and an entire patterning device image is projected in one go(i.e., a single “flash”) onto a target portion C. Substrate table WT canbe shifted in the x and/or y directions so that a different targetportion C can be irradiated by beam PB.

In scan mode, essentially the same scenario applies, except that a giventarget portion C is not exposed in a single “flash.” Instead, patterningdevice table MT is movable in a given direction (the so-called “scandirection”, e.g., the y direction) with a speed v, so that projectionbeam B is caused to scan over a patterning device image; concurrently,substrate table WT is simultaneously moved in the same or oppositedirection at a speed V=Mv, in which M is the magnification of the lensPL (typically, M=¼ or ⅕). In this manner, a relatively large targetportion C can be exposed, without having to compromise on resolution.

FIG. 14 is a schematic diagram of another lithographic projectionapparatus (LPA), according to an embodiment.

LPA can include source collector module SO, illumination system(illuminator) IL configured to condition a radiation beam B (e.g. EUVradiation), support structure MT, substrate table WT, and projectionsystem PS.

Support structure (e.g. a patterning device table) MT can be constructedto support a patterning device (e.g. a mask or a reticle) MA andconnected to a first positioner PM configured to accurately position thepatterning device;

Substrate table (e.g. a wafer table) WT can be constructed to hold asubstrate (e.g. a resist coated wafer) W and connected to a secondpositioner PW configured to accurately position the substrate.

Projection system (e.g. a reflective projection system) PS can beconfigured to project a pattern imparted to the radiation beam B bypatterning device MA onto a target portion C (e.g. comprising one ormore dies) of the substrate W.

As here depicted, LPA can be of a reflective type (e.g. employing areflective patterning device). It is to be noted that because mostmaterials are absorptive within the EUV wavelength range, the patterningdevice may have multilayer reflectors comprising, for example, amulti-stack of molybdenum and silicon. In one example, the multi-stackreflector has a 40 layer pairs of molybdenum and silicon where thethickness of each layer is a quarter wavelength. Even smallerwavelengths may be produced with X-ray lithography. Since most materialis absorptive at EUV and x-ray wavelengths, a thin piece of patternedabsorbing material on the patterning device topography (e.g., a TaNabsorber on top of the multi-layer reflector) defines where featureswould print (positive resist) or not print (negative resist).

Illuminator IL can receive an extreme ultra violet radiation beam fromsource collector module SO. Methods to produce EUV radiation include,but are not necessarily limited to, converting a material into a plasmastate that has at least one element, e.g., xenon, lithium or tin, withone or more emission lines in the EUV range. In one such method, oftentermed laser produced plasma (“LPP”) the plasma can be produced byirradiating a fuel, such as a droplet, stream or cluster of materialhaving the line-emitting element, with a laser beam. Source collectormodule SO may be part of an EUV radiation system including a laser forproviding the laser beam exciting the fuel. The resulting plasma emitsoutput radiation, e.g., EUV radiation, which is collected using aradiation collector, disposed in the source collector module. The laserand the source collector module may be separate entities, for examplewhen a CO2 laser is used to provide the laser beam for fuel excitation.

In such cases, the laser may not be considered to form part of thelithographic apparatus and the radiation beam can be passed from thelaser to the source collector module with the aid of a beam deliverysystem comprising, for example, suitable directing mirrors and/or a beamexpander. In other cases, the source may be an integral part of thesource collector module, for example when the source is a dischargeproduced plasma EUV generator, often termed as a DPP source.

Illuminator IL may comprise an adjuster for adjusting the angularintensity distribution of the radiation beam. Generally, at least theouter and/or inner radial extent (commonly referred to as G-outer andG-inner, respectively) of the intensity distribution in a pupil plane ofthe illuminator can be adjusted. In addition, the illuminator IL maycomprise various other components, such as facetted field and pupilmirror devices. The illuminator may be used to condition the radiationbeam, to have a desired uniformity and intensity distribution in itscross section.

The radiation beam B can be incident on the patterning device (e.g.,mask) MA, which is held on the support structure (e.g., patterningdevice table) MT, and is patterned by the patterning device. After beingreflected from the patterning device (e.g. mask) MA, the radiation beamB passes through the projection system PS, which focuses the beam onto atarget portion C of the substrate W. With the aid of the secondpositioner PW and position sensor PS2 (e.g. an interferometric device,linear encoder or capacitive sensor), the substrate table WT can bemoved accurately, e.g. so as to position different target portions C inthe path of radiation beam B. Similarly, the first positioner PM andanother position sensor PS1 can be used to accurately position thepatterning device (e.g. mask) MA with respect to the path of theradiation beam B. Patterning device (e.g. mask) MA and substrate W maybe aligned using patterning device alignment marks M1, M2 and substratealignment marks P1, P2.

The depicted apparatus LPA could be used in at least one of thefollowing modes, step mode, scan mode, and stationary mode.

In step mode, the support structure (e.g. patterning device table) MTand the substrate table WT are kept essentially stationary, while anentire pattern imparted to the radiation beam is projected onto a targetportion C at one time (i.e. a single static exposure). The substratetable WT is then shifted in the X and/or Y direction so that a differenttarget portion C can be exposed.

In scan mode, the support structure (e.g. patterning device table) MTand the substrate table WT are scanned synchronously while a patternimparted to the radiation beam is projected onto target portion C (i.e.a single dynamic exposure). The velocity and direction of substratetable WT relative to the support structure (e.g. patterning devicetable) MT may be determined by the (de-) magnification and imagereversal characteristics of the projection system PS.

In stationary mode, the support structure (e.g. patterning device table)MT is kept essentially stationary holding a programmable patterningdevice, and substrate table WT is moved or scanned while a patternimparted to the radiation beam is projected onto a target portion C. Inthis mode, generally a pulsed radiation source is employed and theprogrammable patterning device is updated as required after eachmovement of the substrate table WT or in between successive radiationpulses during a scan. This mode of operation can be readily applied tomaskless lithography that utilizes programmable patterning device, suchas a programmable mirror array of a type as referred to above.

FIG. 15 is a detailed view of the lithographic projection apparatus,according to an embodiment.

As shown, LPA can include the source collector module SO, theillumination system IL, and the projection system PS. The sourcecollector module SO is constructed and arranged such that a vacuumenvironment can be maintained in an enclosing structure 220 of thesource collector module

SO. An EUV radiation emitting plasma 210 may be formed by a dischargeproduced plasma source. EUV radiation may be produced by a gas or vapor,for example Xe gas, Li vapor or Sn vapor in which the very hot plasma210 is created to emit radiation in the EUV range of the electromagneticspectrum. The very hot plasma 210 is created by, for example, anelectrical discharge causing at least partially ionized plasma. Partialpressures of, for example, 10 Pa of Xe, Li, Sn vapor or any othersuitable gas or vapor may be required for efficient generation of theradiation. In an embodiment, a plasma of excited tin (Sn) is provided toproduce EUV radiation.

The radiation emitted by the hot plasma 210 is passed from a sourcechamber 211 into a collector chamber 212 via an optional gas barrier orcontaminant trap 230 (in some cases also referred to as contaminantbarrier or foil trap) which is positioned in or behind an opening insource chamber 211. The contaminant trap 230 may include a channelstructure. Contamination trap 230 may also include a gas barrier or acombination of a gas barrier and a channel structure. The contaminanttrap or contaminant barrier 230 further indicated herein at leastincludes a channel structure, as known in the art.

The collector chamber 211 may include a radiation collector CO which maybe a so-called grazing incidence collector. Radiation collector CO hasan upstream radiation collector side 251 and a downstream radiationcollector side 252. Radiation that traverses collector CO can bereflected off a grating spectral filter 240 to be focused in a virtualsource point IF along the optical axis indicated by the dot-dashed line‘0’. The virtual source point IF is commonly referred to as theintermediate focus, and the source collector module is arranged suchthat the intermediate focus IF is located at or near an opening 221 inthe enclosing structure 220. The virtual source point IF is an image ofthe radiation emitting plasma 210.

Subsequently the radiation traverses the illumination system IL, whichmay include a facetted field mirror device 22 and a facetted pupilmirror device 24 arranged to provide a desired angular distribution ofthe radiation beam 21, at the patterning device MA, as well as a desireduniformity of radiation intensity at the patterning device MA. Uponreflection of the beam of radiation 21 at the patterning device MA, heldby the support structure MT, a patterned beam 26 is formed and thepatterned beam 26 is imaged by the projection system PS via reflectiveelements 28, 30 onto a substrate W held by the substrate table WT.

More elements than shown may generally be present in illumination opticsunit IL and projection system PS. The grating spectral filter 240 mayoptionally be present, depending upon the type of lithographicapparatus. Further, there may be more mirrors present than those shownin the figures, for example there may be 1-6 additional reflectiveelements present in the projection system PS than shown in FIG. 13 .

Collector optic CO, as illustrated in FIG. 13 , is depicted as a nestedcollector with grazing incidence reflectors 253, 254 and 255, just as anexample of a collector (or collector mirror). The grazing incidencereflectors 253, 254 and 255 are disposed axially symmetric around theoptical axis O and a collector optic CO of this type may be used incombination with a discharge produced plasma source, often called a DPPsource.

FIG. 16 is a detailed view of source collector module SO of lithographicprojection apparatus LPA, according to an embodiment.

Source collector module SO may be part of an LPA radiation system. Alaser LA can be arranged to deposit laser energy into a fuel, such asxenon (Xe), tin (Sn) or lithium (Li), creating the highly ionized plasma210 with electron temperatures of several 10's of eV. The energeticradiation generated during de-excitation and recombination of these ionsis emitted from the plasma, collected by a near normal incidencecollector optic CO and focused onto the opening 221 in the enclosingstructure 220.

The concepts disclosed herein may simulate or mathematically model anygeneric imaging system for imaging sub wavelength features, and may beespecially useful with emerging imaging technologies capable ofproducing increasingly shorter wavelengths. Emerging technologiesalready in use include EUV (extreme ultra violet), DUV lithography thatis capable of producing a 193 nm wavelength with the use of an ArFlaser, and even a 157 nm wavelength with the use of a Fluorine laser.Moreover, EUV lithography is capable of producing wavelengths within arange of 20-50 nm by using a synchrotron or by hitting a material(either solid or a plasma) with high energy electrons in order toproduce photons within this range.

FIG. 17 schematically depicts an embodiment of an electron beaminspection apparatus 2320, according to an embodiment. In an embodiment,the inspection apparatus may be an electron beam inspection apparatus(e.g., the same as or similar to a scanning electron microscope (SEM))that yields an image of a structure (e.g., some or all the structure ofa device, such as an integrated circuit) exposed or transferred on thesubstrate. A primary electron beam 2324 emitted from an electron source2322 is converged by condenser lens 2326 and then passes through a beamdeflector 2328, an E×B deflector 2330, and an objective lens 2332 toirradiate a substrate 2310 on a substrate table 2312 at a focus.

When the substrate 2310 is irradiated with electron beam 2324, secondaryelectrons are generated from the substrate 2310. The secondary electronsare deflected by the E×B deflector 2330 and detected by a secondaryelectron detector 2334. A two-dimensional electron beam image can beobtained by detecting the electrons generated from the sample insynchronization with, e.g., two dimensional scanning of the electronbeam by beam deflector 2328 or with repetitive scanning of electron beam2324 by beam deflector 2328 in an X or Y direction, together withcontinuous movement of the substrate 2310 by the substrate table 2312 inthe other of the X or Y direction. Thus, in an embodiment, the electronbeam inspection apparatus has a field of view for the electron beamdefined by the angular range into which the electron beam can beprovided by the electron beam inspection apparatus (e.g., the angularrange through which the deflector 2328 can provide the electron beam2324). Thus, the spatial extent of the field of the view is the spatialextent to which the angular range of the electron beam can impinge on asurface (wherein the surface can be stationary or can move with respectto the field).

A signal detected by secondary electron detector 2334 is converted to adigital signal by an analog/digital (A/D) converter 2336, and thedigital signal is sent to an image processing system 2350. In anembodiment, the image processing system 2350 may have memory 2356 tostore all or part of digital images for processing by a processing unit2358. The processing unit 2358 (e.g., specially designed hardware or acombination of hardware and software or a computer readable mediumcomprising software) is configured to convert or process the digitalimages into datasets representative of the digital images. In anembodiment, the processing unit 2358 is configured or programmed tocause execution of a method described herein. Further, image processingsystem 2350 may have a storage medium 2356 configured to store thedigital images and corresponding datasets in a reference database. Adisplay device 2354 may be connected with the image processing system2350, so that an operator can conduct necessary operation of theequipment with the help of a graphical user interface.

FIG. 18 schematically illustrates a further embodiment of an inspectionapparatus, according to an embodiment. The system is used to inspect asample 90 (such as a substrate) on a sample stage 88 and comprises acharged particle beam generator 81, a condenser lens module 82, a probeforming objective lens module 83, a charged particle beam deflectionmodule 84, a secondary charged particle detector module 85, and an imageforming module 86.

The charged particle beam generator 81 generates a primary chargedparticle beam 91. The condenser lens module 82 condenses the generatedprimary charged particle beam 91. The probe forming objective lensmodule 83 focuses the condensed primary charged particle beam into acharged particle beam probe 92. The charged particle beam deflectionmodule 84 scans the formed charged particle beam probe 92 across thesurface of an area of interest on the sample 90 secured on the samplestage 88. In an embodiment, the charged particle beam generator 81, thecondenser lens module 82 and the probe forming objective lens module 83,or their equivalent designs, alternatives or any combination thereof,together form a charged particle beam probe generator which generatesthe scanning charged particle beam probe 92.

The secondary charged particle detector module 85 detects secondarycharged particles 93 emitted from the sample surface (maybe also alongwith other reflected or scattered charged particles from the samplesurface) upon being bombarded by the charged particle beam probe 92 togenerate a secondary charged particle detection signal 94. The imageforming module 86 (e.g., a computing device) is coupled with thesecondary charged particle detector module 85 to receive the secondarycharged particle detection signal 94 from the secondary charged particledetector module 85 and accordingly forming at least one scanned image.In an embodiment, the secondary charged particle detector module 85 andimage forming module 86, or their equivalent designs, alternatives orany combination thereof, together form an image forming apparatus whichforms a scanned image from detected secondary charged particles emittedfrom sample 90 being bombarded by the charged particle beam probe 92.

In an embodiment, a monitoring module 87 is coupled to the image formingmodule 86 of the image forming apparatus to monitor, control, etc. thepatterning process and/or derive a parameter for patterning processdesign, control, monitoring, etc. using the scanned image of the sample90 received from image forming module 86. So, in an embodiment, themonitoring module 87 is configured or programmed to cause execution of amethod described herein. In an embodiment, the monitoring module 87comprises a computing device. In an embodiment, the monitoring module 87comprises a computer program to provide functionality herein and encodedon a computer readable medium forming, or disposed within, themonitoring module 87.

In an embodiment, like the electron beam inspection tool of FIG. 19 thatuses a probe to inspect a substrate, the electron current in the systemof FIG. 20 is significantly larger compared to, e.g., a CD SEM such asdepicted in FIG. 19 , such that the probe spot is large enough so thatthe inspection speed can be fast. However, the resolution may not be ashigh as compared to a CD SEM because of the large probe spot.

The SEM images, from, e.g., the system of FIG. 19 and/or FIG. 20 , maybe processed to extract contours that describe the edges of objects,representing device structures, in the image These contours are thentypically quantified via metrics, such as CD, at user-defined cut-lines.Thus, typically, the images of device structures are compared andquantified via metrics, such as an edge-to-edge distance (CD) measuredon extracted contours or simple pixel differences between images.Alternatively, metrics can include EP gauges as described herein.

Now, besides measuring substrates in a patterning process, it is oftendesirable to use one or more tools to produce results that, for example,can be used to design, control, monitor, etc. the patterning process. Todo this, there may be provided one or more tools used in computationallycontrolling, designing, etc. one or more aspects of the patterningprocess, such as the pattern design for a patterning device (including,for example, adding sub-resolution assist features or optical proximitycorrections), the illumination for the patterning device, etc.Accordingly, in a system for computationally controlling, designing,etc. a manufacturing process involving patterning, the majormanufacturing system components and/or processes can be described byvarious functional modules. In particular, in an embodiment, one or moremathematical models can be provided that describe one or more stepsand/or apparatuses of the patterning process, including typically thepattern transfer step. In an embodiment, a simulation of the patterningprocess can be performed using one or more mathematical models tosimulate how the patterning process forms a patterned substrate using ameasured or design pattern provided by a patterning device.

While the concepts disclosed herein may be used for imaging on asubstrate such as a silicon wafer, it shall be understood that thedisclosed concepts may be used with any type of lithographic imagingsystems, e.g., those used for imaging on substrates other than siliconwafers.

FIG. 19 depicts an example inspection apparatus (e.g., a scatterometer).It comprises a broadband (white light) radiation projector 2 whichprojects radiation onto a substrate W. The redirected radiation ispassed to a spectrometer detector 4, which measures a spectrum 10(intensity as a function of wavelength) of the specular reflectedradiation, as shown, e.g., in the graph in the lower left. From thisdata, the structure or profile giving rise to the detected spectrum maybe reconstructed by processor PU, e.g. by Rigorous Coupled Wave Analysisand non-linear regression or by comparison with a library of simulatedspectra as shown at the bottom right of FIG. 3 . In general, for thereconstruction the general form of the structure is known and somevariables are assumed from knowledge of the process by which thestructure was made, leaving only a few variables of the structure to bedetermined from the measured data. Such an inspection apparatus may beconfigured as a normal-incidence inspection apparatus or anoblique-incidence inspection apparatus.

Another inspection apparatus that may be used is shown in FIG. 20 . Inthis device, the radiation emitted by radiation source 2 is collimatedusing lens system 12 and transmitted through interference filter 13 andpolarizer 17, reflected by partially reflecting surface 16 and isfocused into a spot S on substrate W via an objective lens 15, which hasa high numerical aperture (NA), desirably at least 0.9 or at least 0.95.An immersion inspection apparatus (using a relatively high refractiveindex fluid such as water) may even have a numerical aperture over 1.

As in the lithographic apparatus LA, one or more substrate tables may beprovided to hold the substrate W during measurement operations. Thesubstrate tables may be similar or identical in form to the substratetable WT of FIG. 1 . In an example where the inspection apparatus isintegrated with the lithographic apparatus, they may even be the samesubstrate table. Coarse and fine positioners may be provided to a secondpositioner PW configured to accurately position the substrate inrelation to a measurement optical system. Various sensors and actuatorsare provided for example to acquire the position of a target ofinterest, and to bring it into position under the objective lens 15.Typically many measurements will be made on targets at differentlocations across the substrate W. The substrate support can be moved inX and Y directions to acquire different targets, and in the Z directionto obtain a desired location of the target relative to the focus of theoptical system. It is convenient to think and describe operations as ifthe objective lens is being brought to different locations relative tothe substrate, when, for example, in practice the optical system mayremain substantially stationary (typically in the X and Y directions,but perhaps also in the Z direction) and only the substrate moves.Provided the relative position of the substrate and the optical systemis correct, it does not matter in principle which one of those is movingin the real world, or if both are moving, or a combination of a part ofthe optical system is moving (e.g., in the Z and/or tilt direction) withthe remainder of the optical system being stationary and the substrateis moving (e.g., in the X and Y directions, but also optionally in the Zand/or tilt direction).

The radiation redirected by the substrate W then passes throughpartially reflecting surface 16 into a detector 18 in order to have thespectrum detected. The detector 18 may be located at a back-projectedfocal plane 11 (i.e., at the focal length of the lens system 15) or theplane 11 may be re-imaged with auxiliary optics (not shown) onto thedetector 18. The detector may be a two-dimensional detector so that atwo-dimensional angular scatter spectrum of a substrate target 30 can bemeasured. The detector 18 may be, for example, an array of CCD or CMOSsensors, and may use an integration time of, for example, 40milliseconds per frame.

A reference beam may be used, for example, to measure the intensity ofthe incident radiation. To do this, when the radiation beam is incidenton the partially reflecting surface 16 part of it is transmitted throughthe partially reflecting surface 16 as a reference beam towards areference mirror 14. The reference beam is then projected onto adifferent part of the same detector 18 or alternatively on to adifferent detector (not shown).

One or more interference filters 13 are available to select a wavelengthof interest in the range of, say, 405-790 nm or even lower, such as200-300 nm. The interference filter may be tunable rather thancomprising a set of different filters. A grating could be used insteadof an interference filter. An aperture stop or spatial light modulator(not shown) may be provided in the illumination path to control therange of angle of incidence of radiation on the target.

The detector 18 may measure the intensity of redirected radiation at asingle wavelength (or narrow wavelength range), the intensity separatelyat multiple wavelengths or integrated over a wavelength range.Furthermore, the detector may separately measure the intensity oftransverse magnetic- and transverse electric-polarized radiation and/orthe phase difference between the transverse magnetic- and transverseelectric-polarized radiation.

The target 30 on substrate W may be a 1-D grating, which is printed suchthat after development, the bars are formed of solid resist lines. Thetarget 30 may be a 2-D grating, which is printed such that afterdevelopment, the grating is formed of solid resist pillars or vias inthe resist.

The bars, pillars or vias may be etched into or on the substrate (e.g.,into one or more layers on the substrate). The pattern (e.g., of bars,pillars or vias) is sensitive to change in processing in the patterningprocess (e.g., optical aberration in the lithographic projectionapparatus (particularly the projection system PS), focus change, dosechange, etc.) and will manifest in a variation in the printed grating.Accordingly, the measured data of the printed grating is used toreconstruct the grating. One or more parameters of the 1-D grating, suchas line width and/or shape, or one or more parameters of the 2-Dgrating, such as pillar or via width or length or shape, may be input tothe reconstruction process, performed by processor PU, from knowledge ofthe printing step and/or other inspection processes.

In addition to measurement of a parameter by reconstruction, angleresolved scatterometry is useful in the measurement of asymmetry offeatures in product and/or resist patterns. A particular application ofasymmetry measurement is for the measurement of overlay, where thetarget 30 comprises one set of periodic features superimposed onanother. The concepts of asymmetry measurement using the instrument ofFIG. 25 or FIG. 26 are described, for example, in U.S. patentapplication publication US2006-066855, which is incorporated herein inits entirety. Simply stated, while the positions of the diffractionorders in the diffraction spectrum of the target are determined only bythe periodicity of the target, asymmetry in the diffraction spectrum isindicative of asymmetry in the individual features which make up thetarget. In the instrument of FIG. 20 , where detector 18 may be an imagesensor, such asymmetry in the diffraction orders appears directly asasymmetry in the pupil image recorded by detector 18. This asymmetry canbe measured by digital image processing in unit PU, and calibratedagainst known values of overlay.

FIG. 21 illustrates a plan view of a typical target 30, and the extentof illumination spot S in the apparatus of FIG. 20 . To obtain adiffraction spectrum that is free of interference from surroundingstructures, the target 30, in an embodiment, is a periodic structure(e.g., grating) larger than the width (e.g., diameter) of theillumination spot S. The width of spot S may be smaller than the widthand length of the target. The target in other words is ‘underfilled’ bythe illumination, and the diffraction signal is essentially free fromany signals from product features and the like outside the targetitself. The illumination arrangement 2, 12, 13, 17 may be configured toprovide illumination of a uniform intensity across a back focal plane ofobjective 15. Alternatively, by, e.g., including an aperture in theillumination path, illumination may be restricted to on axis or off axisdirections.

The embodiments may further be described using the following clauses:

-   1. A non-transitory computer-readable medium having instructions    that, when executed by a computer, cause the computer to execute a    method for training a machine learning model to generate a    characteristic pattern, the method comprising:

obtaining training data associated with a reference feature in areference image, wherein the training data includes (i) location data ofa portion of the reference feature, and (ii) a presence value indicatingwhether the portion of the reference feature is located within areference assist feature generated for the reference feature; and

training, based on the training data, the machine learning model suchthat a metric between a predicted presence value and the presence valueis minimized

-   2. The computer-readable medium of any of clause 1, wherein the    characteristic pattern is used for manufacturing a mask pattern,    which is further used for printing a target pattern on a substrate.-   3. The computer-readable medium of any of clause 2, wherein the    reference image is a continuous transmission mask (CTM) image    generated by simulating an optical proximity correction process    using the target pattern, and wherein the reference feature    corresponds to a target feature from the target pattern.-   4. The computer-readable medium of clause 2, wherein the reference    assist feature includes sub-resolution assist features placed around    the reference feature, the sub-resolution assist features being    rectilinear in shape.-   5. The computer-readable medium of clause 4, wherein the    sub-resolution assist features are rectilinear in shape.-   6. The computer-readable medium of any of clauses 1-5, wherein the    training data includes training data for a plurality of reference    features in one or more reference images.-   7. The computer-readable medium of any of clause 1, wherein the    location data includes location data of each portion of a plurality    of portions of the reference feature.-   8. The computer-readable medium of any of clauses 1-7, wherein    training the machine learning model includes:

a. executing, the machine learning model using the training data, tooutput the predicted presence value associated with the correspondingportion of the reference feature;

b. determining the metric between the predicted presence value and thepresence value;

c. adjusting the machine learning model such that the metric is reduced;

d. determining whether the metric is minimized; and

e. responsive to not minimized, performing steps (a), (b), (c), and (d).

-   9. The computer-readable medium of any of clauses 1-8, the method    further comprising:

obtaining a specified reference image; and

-   -   determining, via executing the machine learning model using the        specified reference image, a preferred assist feature for        placement in relation to a specified feature of the specified        reference image, wherein the specified feature corresponds to a        target feature of a target pattern to be printed on the        substrate.

-   10. The computer-readable medium of clause 9, wherein determining    the preferred assist feature includes:

obtaining, from the specified reference image and using an intensitythreshold, a specified contour of the specified feature,

generating a skeleton of the specified contour,

inputting location data and distance data to the machine learning model,wherein the location data includes coordinates of a set of points on theskeleton, wherein the distance data indicates a closest distance from apoint of the set of points to the specified contour, and

obtaining, from the machine learning model, a predicted presence valuefor each point of the set of points, wherein the predicted presencevalue indicates whether the corresponding point is predicted to belocated within the preferred assist feature, wherein the set of pointsincludes

(a) a covered set of points that is predicted to located within thepreferred assist feature, and

(b) an uncovered set of points that is predicted not to be locatedwithin the preferred assist feature.

-   11. The computer-readable medium of clause 10, the method further    comprising:

generating a plurality of assist feature sets to cover points from thecovered set of points,

determining a reward value for each assist feature set using a scoringfunction, and

determining a first assist feature set of the assist feature sets havinga highest reward value as the preferred assist feature for placement inrelation to the specified contour.

-   12. The computer-readable medium of clause 11, wherein determining    the reward value for each assist feature set includes:    -   (i) selecting a point from the uncovered set of points as a        cut-off point, wherein the cut-off point divides the skeleton        into a plurality of segments,

(ii) generating an assist feature set of the plurality of assist featuresets having a candidate assist feature for each segment of the pluralityof segments, wherein the candidate assist feature is generated based on(a) the distance data associated with each point of the set of points,and (b) a set of constraints the candidate assist feature has to satisfyfor manufacturing of the mask pattern,

(iii) determining a reward value associated with the assist feature setas a function of (a) image intensity value within the assist featureset, and (b) the intensity threshold, and

iterating through steps (i), (ii) and (iii) by selecting a differentcut-off point from the uncovered set of points, generating anotherassist feature set, and determining their corresponding reward value.

-   13. The computer-readable medium of clause 12, wherein the distance    value indicates a closest distance from a point to the specified    contour.-   14. The computer-readable medium of clause 9, the method further    comprising:

generating a characteristic pattern with the preferred assist feature,wherein the characteristic pattern is a pixelated image that includesthe preferred assist feature placed in relation to the specifiedfeature.

-   15. The computer-readable medium of clause 14, wherein generating    the characteristic pattern includes:

generating the characteristic pattern with a plurality of preferredassist features, wherein the preferred assist features are placed inrelation to a plurality of reference features of the specified referenceimage, wherein the preferred assist features are determined by executingthe machine learning model for the reference features.

-   16. The computer-readable medium of clause 15, wherein generating    the characteristic pattern includes:

adjusting the placement of the preferred assist features further basedon a set of constraints related to manufacturing of the mask pattern.

-   17. The computer-readable medium of clause 1, wherein the machine    learning model is a sequence labeling model.-   18. The computer-readable medium of clause 17, wherein the sequence    labeling model includes a Bidirectional Long Short-term Memory    (BiLSTM) network.-   19. The computer-readable medium of clause 1, wherein obtaining the    training data includes:

generating a plurality of assist feature sets for the reference featurebased on a set of constraints for manufacturing of a mask pattern,wherein each assist feature set is associated with a reward value thatis determined based on a specified scoring function,

determining a specified assist feature set of the plurality of assistfeature sets associated with a highest reward value as the referenceassist feature,

determining a status value for each portion of the reference feature asa function of the reward value of the plurality of assist feature setsand a number of assist feature sets in which the corresponding portionis determined to be located within, and

generating the location data and the presence value of the training datafor each portion of the reference feature, wherein the presence value isset to a first value if the status value of the corresponding portionsatisfies a status threshold, the first value indicating that thecorresponding portion is located within the reference assist feature.

-   20. The computer-readable medium of clause 19, wherein generating    the presence value includes:

a. setting the presence value to a second value if the status value ofthe corresponding portion does not satisfy the status threshold, thesecond value indicating that the corresponding portion is not locatedwithin the reference assist feature. 21. The computer-readable medium ofclause 19, wherein generating the plurality of assist feature setsincludes:

generating a skeleton of the reference feature,

selecting a plurality of cut-off points on the skeleton, wherein eachcut-off point segments the skeleton into a plurality of segments, and

for each cut-off point, generating an assist feature set having areference assist feature for each segment of the plurality of segments,wherein the assist feature set is generated based on the set ofconstraints and a distance value associated with each point of a set ofpoints on the skeleton.

-   22. The computer-readable medium of clause 21, wherein determining    the specified assist feature set having the highest reward value    includes:

determining, using the specified scoring function, the reward value ofan assist feature set of the plurality of assist feature sets as afunction of (a) image intensity value within the assist feature set, and(b) an intensity threshold.

-   23. The computer-readable medium of clause 22, wherein the intensity    threshold is used to generate a contour of the reference feature,    wherein the contour is used to generate the skeleton of the    reference feature.-   24. The computer-readable medium of clause 21, wherein determining    the status value for each portion of the reference feature includes:

determining the status value for each point on the skeleton.

-   25. The computer-readable medium of clause 24, the method further    comprising:

determining the status threshold as a function of a maximum and/orminimum of the status values of the set of points on the skeleton.

-   26. The computer-readable medium of clause 21, wherein generating    the training data for each portion of the reference feature    includes:

generating the location data and the presence value for each point onthe skeleton of the reference feature.

-   27. A non-transitory computer-readable medium having instructions    that, when executed by a computer, cause the computer to execute a    method for generating a characteristic pattern, the method    comprising:

obtaining a contour of a reference feature from a reference image;

executing, by a hardware computer system and using the contour, amachine learning model for determining a preferred assist feature set tobe placed around the contour, and wherein the preferred assist featureset has a reward value that is highest among reward values of aplurality of assist feature sets, and wherein the reward value iscalculated as a function of an intensity threshold used to generate thecontour; and

generating the characteristic pattern with the contour and the preferredassist feature set.

-   28. The computer-readable medium of clause 27, wherein the    characteristic pattern is used for manufacturing a mask pattern that    is used for printing a target pattern on a substrate.-   29. The computer-readable medium of clause 27, wherein the reference    image is a CTM image.-   30. The computer-readable medium of clause 27, wherein executing the    machine learning model to determine the preferred assist feature set    includes:

generating a skeleton of the contour, wherein the skeleton includes aset of points,

selecting a plurality of cut-off points on the skeleton, wherein eachcut-off point segments the skeleton into a plurality of segments, and

for each cut-off point, generating an assist feature set of theplurality of assist feature sets, wherein the assist feature set has anassist feature for each segment of the plurality of segments, whereinthe assist feature set is generated based on a set of constraints and adistance value associated with each point on the skeleton.

-   31. The computer-readable medium of clause 30, the method further    comprising:

determining the reward value of the assist feature set as a function of(a) intensity value associated with each point of the skeleton that islocated within the assist feature set, and (b) the intensity threshold,and

selecting one of the assist feature sets having a highest reward valueas the preferred assist feature set.

-   32. The computer-readable medium of clause 30 further comprising:

a. generating, using the preferred assist feature set, training data fortraining a second machine learning model to generate a secondcharacteristic pattern based on a second reference image.

-   33. The computer-readable medium of clause 32, wherein the training    data includes training data for a plurality of preferred assist    feature sets generated for a plurality of contours from the    reference image.-   34. The computer-readable medium of clause 33, wherein generating    the training data includes:

generating coordinates of each point of the skeleton of the contour, and

generating a presence value associated with each point of the skeleton,wherein the presence value indicates whether the corresponding point islocated within the preferred assist feature set.

-   35. The computer-readable medium of clause 34, wherein generating    the coordinates of each point includes generating coordinates of a    pixel corresponding to the point in the reference image.-   36. The computer-readable medium of clause 34, wherein generating    the presence value includes:

determining a status value for each point of the skeleton as a functionof the reward value of the plurality of assist feature sets and a numberof assist feature sets in which the corresponding point is determined tobe located within,

determining a status threshold as a function of maximum status value anda minimum status value of the set of points of the skeleton, and

generating the presence value for each point of the skeleton, whereinthe presence value is set to a first value if the status value of thecorresponding point satisfies the status threshold, the first valueindicating that the corresponding point is located within the preferredassist feature set.

-   37. The computer-readable medium of clause 32, the method further    comprising:

training, based on the training data, the second machine learning modelsuch that a cost function that determines a difference between apredicted presence value and the presence value is minimized

-   38. A non-transitory computer-readable medium having instructions    that, when executed by a computer, cause the computer to execute a    method for generating a characteristic pattern for a mask pattern,    the method comprising:

obtaining a reference image having reference features;

obtaining a contour of a reference feature of the reference featuresfrom the reference image;

generating a skeleton of the contour;

determining, via executing a machine learning model using the skeleton,a presence value indicating whether each point of a set of points on theskeleton is located within a preferred assist feature set to begenerated for placement around the reference feature; and

generating a characteristic pattern using the presence value.

-   39. The computer-readable medium of clause 38, wherein the    characteristic pattern is a pixelated image that includes the    preferred assist feature set placed in relation to the contour.-   40. The computer-readable medium of clause 38, wherein the set of    points includes (a) a covered set of points that is predicted to    located within the preferred assist feature set, and (b) an    uncovered set of points that is predicted not to be located within    the preferred assist feature set.-   41. The computer-readable medium of clause 40, wherein generating    the characteristic pattern using the presence value includes:

(i) selecting a point from the uncovered set of points as a cut-offpoint, wherein the cut-off point divides the skeleton into a pluralityof segments,

-   -   (ii) generating a first assist feature set having an assist        feature for each segment of the plurality of segments, wherein        the assist feature is generated based on (a) a distance value        associated with each point of the set of points, and (b) a set        of constraints the reference assist feature has to satisfy for        manufacturing of the mask pattern,    -   (iii) determining a reward value associated with the first        assist feature set as a function of (a) intensity value        associated with each point located within the first assist        feature set, and (b) an intensity threshold that is used in        obtaining the contour,    -   iterating through steps (i), (ii) and (iii) by selecting a        different cut-off point from the uncovered set of points,        generating another assist feature set, and determining their        corresponding reward value, and    -   determining one of the assist feature sets that has a highest        reward value as the preferred assist feature set for placement        in relation to the reference feature.

-   42. The computer-readable medium of clause 41, wherein generating    the first assist feature set includes performing a random    perturbation on the first assist feature set and applying the set of    constraints to the first assist feature set.

-   43. The computer-readable medium of clause 38, wherein generating    the characteristic pattern includes generating the characteristic    pattern with a plurality of preferred assist feature sets for    placement in relation to a plurality of reference features from the    reference image.

-   44. The computer-readable medium of clause 38, wherein the reference    image is a CTM image.

-   45. A method for training a machine learning model to generate a    characteristic pattern for a mask pattern, the method comprising:

obtaining training data associated with a reference feature in areference image used in generating the mask pattern, wherein thetraining data includes (i) location data of each portion of a pluralityof portions of the reference feature, and (ii) a presence valueindicating whether the portion of the reference feature is locatedwithin a reference assist feature generated for the reference feature;and

training, by a hardware computer system and based on the training dataassociated with the reference feature, the machine learning model suchthat a metric between a predicted presence value and the presence valueis minimized

-   46. A method for generating a characteristic pattern for a mask    pattern, the method comprising:

obtaining a contour of a reference feature from a reference image; and

executing, by a hardware computer system and using the contour, amachine learning model for determining a preferred assist feature to beplaced around the contour, and wherein the preferred assist feature hasa reward value that is highest among reward values of a plurality ofreference assist features, and wherein the reward value is calculated asa function of an intensity threshold used to generate the contour; and

generating the characteristic pattern with the contour and the preferredassist feature.

-   47. A method for generating a characteristic pattern for a mask    pattern, the method comprising:

obtaining a reference image having reference features;

obtaining a contour of a reference feature from the reference image;

generating a skeleton of the contour;

determining, by a hardware system and via executing a machine learningmodel using the skeleton, a presence value indicating whether each pointof a set of points on the skeleton is located within a preferred assistfeature to be generated for placement around the reference feature; and

generating a characteristic pattern using the presence value.

-   48. A non-transitory computer-readable medium having instructions    recorded thereon, the instructions when executed by a computer    implementing the method of any of the above clauses.

The descriptions above are intended to be illustrative, not limiting.Thus, it will be apparent to one skilled in the art that modificationsmay be made as described without departing from the scope of the claimsset out below.

1. A non-transitory computer-readable medium having instructions thereinthat, when executed by a computer system, are configured to cause thecomputer to at least: obtain training data associated with a referencefeature in a reference image, wherein the training data includes (i)location data of a portion of the reference feature, and (ii) a presencevalue indicating whether the portion of the reference feature is locatedwithin a reference assist feature generated for the reference feature;and train, based on the training data, a machine learning modelconfigured to generate a characteristic pattern, such that a metricbetween a predicted presence value and the presence value is minimized.2. The computer-readable medium of claim 1, wherein the reference imageis a continuous transmission mask (CTM) image generated by simulation ofan optical proximity correction process using a target pattern, andwherein the reference feature corresponds to a target feature from thetarget pattern.
 3. The computer-readable medium of claim 1, wherein thereference assist feature includes one or more sub-resolution assistfeatures placed around the reference feature, the one or moresub-resolution assist features being rectilinear in shape.
 4. Thecomputer-readable medium of claim 1, wherein the training data includestraining data for a plurality of reference features in one or morereference images.
 5. The computer-readable medium of claim 1, whereinthe location data includes location data of each portion of a pluralityof portions of the reference feature.
 6. The computer-readable medium ofclaim 1, wherein the instructions configured to cause the computersystem to train the machine learning model are further configured tocause the computer system to: (a) execute the machine learning model,using the training data, to output the predicted presence valueassociated with the corresponding portion of the reference feature; (b)determine the metric between the predicted presence value and thepresence value; (c) adjust the machine learning model such that themetric is reduced; (d) determine whether the metric is minimized; and(e) responsive to the metric not being minimized, perform (a), (b), (c),and (d).
 7. The computer-readable medium of claim 1, wherein theinstructions are further configured to cause the computer system to:obtain a specified reference image; and determine, via execution of themachine learning model using the specified reference image, a preferredassist feature for placement in relation to a specified feature of thespecified reference image, wherein the specified feature corresponds toa target feature of a target pattern to be printed on the substrate. 8.The computer-readable medium of claim 16, wherein the instructions arefurther configured to cause the computer system to: generate a pluralityof assist feature sets to cover points from the covered set of points,determine a reward value for each assist feature set using a scoringfunction, and determine a first assist feature set of the assist featuresets having a highest reward value as the preferred assist feature forplacement in relation to the specified contour.
 9. The computer-readablemedium of claim 7, wherein the instructions are further configured tocause the computer system to generate a characteristic pattern with thepreferred assist feature, wherein the characteristic pattern is apixelated image that includes the preferred assist feature placed inrelation to the specified feature.
 10. The computer-readable medium ofclaim 9, wherein the instructions configured to cause the computersystem to generate the characteristic pattern are further configured tocause the computer system to generate the characteristic pattern with aplurality of preferred assist features, wherein the preferred assistfeatures are placed in relation to a plurality of reference features ofthe specified reference image, and wherein the preferred assist featuresare determined by execution of the machine learning model for thereference features.
 11. The computer-readable medium of claim 1, whereinthe instructions configured to cause the computer system to obtain thetraining data are further configured to cause the computer system to:generate a plurality of assist feature sets for the reference featurebased on a set of constraints for manufacturing of a mask pattern,wherein each assist feature set is associated with a reward value thatis determined based on a specified scoring function, determine aspecified assist feature set of the plurality of assist feature setsassociated with a highest reward value as the reference assist feature,determine a status value for each portion of the reference feature as afunction of the reward value of the plurality of assist feature sets anda number of assist feature sets in which the corresponding portion isdetermined to be located within, and generate the location data and thepresence value of the training data for each portion of the referencefeature, wherein the presence value is set to a first value if thestatus value of the corresponding portion satisfies a status threshold,the first value indicating that the corresponding portion is locatedwithin the reference assist feature.
 12. The computer-readable medium ofclaim 11, wherein the instructions configured to cause the computersystem to generate the presence value are further configured to causethe computer system to set: the presence value to a second value if thestatus value of the corresponding portion does not satisfy the statusthreshold, the second value indicating that the corresponding portion isnot located within the reference assist feature.
 13. Thecomputer-readable medium of claim 11, wherein the instructionsconfigured to cause the computer system to generate the plurality ofassist feature sets are further configured to cause the computer systemto: generate a skeleton of the reference feature, select a plurality ofcut-off points on the skeleton, wherein each cut-off point segments theskeleton into a plurality of segments, and for each cut-off point,generate an assist feature set having a reference assist feature foreach segment of the plurality of segments, wherein the assist featureset is generated based on the set of constraints and a distance valueassociated with each point of a set of points on the skeleton.
 14. Thecomputer-readable medium of claim 13, wherein the instructionsconfigured to cause the computer system to determine the specifiedassist feature set having the highest reward value are furtherconfigured to cause the computer system to determine, using thespecified scoring function, the reward value of an assist feature set ofthe plurality of assist feature sets as a function of (a) imageintensity value within the assist feature set, and (b) an intensitythreshold.
 15. The computer-readable medium of claim 13, wherein theinstructions configured to cause the computer system to generate thetraining data for each portion of the reference feature are furtherconfigured to cause the computer system to generate the location dataand the presence value for each point on the skeleton of the referencefeature.
 16. The computer-readable medium of claim 7, wherein theinstructions configured to cause the computer system to determine thepreferred assist feature are further configured to cause the computersystem to: obtain, from the specified reference image and using anintensity threshold, a specified contour of the specified feature,generate a skeleton of the specified contour, input location data anddistance data to the machine learning model, wherein the location dataincludes coordinates of a set of points on the skeleton and the distancedata indicates a closest distance from a point of the set of points tothe specified contour, and obtain, from the machine learning model, apredicted presence value for each point of the set of points, whereinthe predicted presence value indicates whether the corresponding pointis predicted to be located within the preferred assist feature.
 17. Amethod for training a machine learning model to generate acharacteristic pattern, the method comprising: obtaining training dataassociated with a reference feature in a reference image, wherein thetraining data includes (i) location data of a portion of the referencefeature, and (ii) a presence value indicating whether the portion of thereference feature is located within a reference assist feature generatedfor the reference feature; and training, based on the training data, themachine learning model such that a metric between a predicted presencevalue and the presence value is minimized.
 18. The method of claim 17,wherein the reference image is a continuous transmission mask (CTM)image generated by simulation of an optical proximity correction processusing a target pattern, and wherein the reference feature corresponds toa target feature from the target pattern.
 19. The method of claim 17,further comprising: obtaining a specified reference image; anddetermining, via executing the machine learning model using thespecified reference image, a preferred assist feature for placement inrelation to a specified feature of the specified reference image,wherein the specified feature corresponds to a target feature of atarget pattern to be printed on the substrate.
 20. The method of claim17, wherein the obtaining the training data includes: generating aplurality of assist feature sets for the reference feature based on aset of constraints for manufacturing of a mask pattern, wherein eachassist feature set is associated with a reward value that is determinedbased on a specified scoring function, determining a specified assistfeature set of the plurality of assist feature sets associated with ahighest reward value as the reference assist feature, determining astatus value for each portion of the reference feature as a function ofthe reward value of the plurality of assist feature sets and a number ofassist feature sets in which the corresponding portion is determined tobe located within, and generating the location data and the presencevalue of the training data for each portion of the reference feature,wherein the presence value is set to a first value if the status valueof the corresponding portion satisfies a status threshold, the firstvalue indicating that the corresponding portion is located within thereference assist feature.